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pkuAI4M
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lean_github

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Split (1)

train · 219k rows

url stringclasses 147 values	commit stringclasses 147 values	file_path stringlengths 7 101	full_name stringlengths 1 94	start stringlengths 6 10	end stringlengths 6 11	tactic stringlengths 1 11.2k	state_before stringlengths 3 2.09M	state_after stringlengths 6 2.09M	input stringlengths 73 2.09M
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	rw [Nat.add_assoc]	case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ Nat.succ 0 < 1 + sizeOf l✝ + sizeOf r✝	case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝)	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ Nat.succ 0 < 1 + sizeOf l✝ + sizeOf r✝ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	apply Nat.lt_add_of_pos_right	case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝)	case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝) TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	first \| (apply Nat.add_pos_left; apply sizeOf_pos) \| (apply Nat.add_pos_right; apply sizeOf_pos)	case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝	no goals	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	(apply Nat.add_pos_left; apply sizeOf_pos)	case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝	case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	apply Nat.add_pos_left	case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝	case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	apply sizeOf_pos	case mp.semiL.h.h P✝ : Sort u_1 b : Bunch P✝ l✝ : BunchWithHole P✝ r✝ : Bunch P✝ h : (subst b l✝ ;ᵇ r✝) = b ⊢ 0 < sizeOf l✝	no goals	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiL.h.h P✝ : Sort u_1 b : Bunch P✝ l✝ : BunchWithHole P✝ r✝ : Bunch P✝ h : (subst b l✝ ;ᵇ r✝) = b ⊢ 0 < sizeOf l✝ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	(apply Nat.add_pos_right; apply sizeOf_pos)	case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝	no goals	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	apply Nat.add_pos_right	case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝	case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf r✝	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	apply sizeOf_pos	case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf r✝	no goals	Please generate a tactic in lean4 to solve the state. STATE: case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf r✝ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	rintro rfl	case mpr P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ Γ = hole → subst b Γ = b	case mpr P✝ : Sort u_1 b : Bunch P✝ ⊢ subst b hole = b	Please generate a tactic in lean4 to solve the state. STATE: case mpr P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ Γ = hole → subst b Γ = b TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.subst_idem	[101, 9]	[116, 21]	simp	case mpr P✝ : Sort u_1 b : Bunch P✝ ⊢ subst b hole = b	no goals	Please generate a tactic in lean4 to solve the state. STATE: case mpr P✝ : Sort u_1 b : Bunch P✝ ⊢ subst b hole = b TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.idem_subst	[118, 9]	[120, 7]	rw [eq_comm]	P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ b = subst b Γ ↔ Γ = hole	P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ subst b Γ = b ↔ Γ = hole	Please generate a tactic in lean4 to solve the state. STATE: P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ b = subst b Γ ↔ Γ = hole TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.idem_subst	[118, 9]	[120, 7]	simp	P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ subst b Γ = b ↔ Γ = hole	no goals	Please generate a tactic in lean4 to solve the state. STATE: P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ subst b Γ = b ↔ Γ = hole TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.comp_hole	[148, 9]	[149, 30]	induction Γ <;> simp_all	P : Sort u_1 Γ : BunchWithHole P ⊢ Γ.comp hole = Γ	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 Γ : BunchWithHole P ⊢ Γ.comp hole = Γ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.comp_def	[151, 1]	[153, 55]	induction h1 <;> simp_all [comp, FunLike.coe, subst]	P : Sort u_1 h1 h2 : BunchWithHole P b : Bunch P ⊢ ↑(h1.comp h2) b = ↑h1 (↑h2 b)	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 h1 h2 : BunchWithHole P b : Bunch P ⊢ ↑(h1.comp h2) b = ↑h1 (↑h2 b) TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_prop	[155, 9]	[157, 40]	cases Γ <;> simp [FunLike.coe, subst]	P : Sort u_1 b : Bunch P φ : Typ P Γ : BunchWithHole P ⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b : Bunch P φ : Typ P Γ : BunchWithHole P ⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.prop_eq	[159, 9]	[162, 7]	rw [show (prop φ = _ ↔ _ = prop φ) from ⟨Eq.symm, Eq.symm⟩]	P : Sort u_1 φ : Typ P b : Bunch P Γ : BunchWithHole P ⊢ prop φ = ↑Γ b ↔ Γ = hole ∧ b = prop φ	P : Sort u_1 φ : Typ P b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ : Typ P b : Bunch P Γ : BunchWithHole P ⊢ prop φ = ↑Γ b ↔ Γ = hole ∧ b = prop φ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.prop_eq	[159, 9]	[162, 7]	simp	P : Sort u_1 φ : Typ P b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ : Typ P b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_cunit	[164, 9]	[166, 40]	cases Γ <;> simp [FunLike.coe, subst]	P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.cunit_eq	[168, 9]	[171, 7]	rw [show (_ = _ ↔ _ = _) from ⟨Eq.symm, Eq.symm⟩]	P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ cunit = ↑Γ b ↔ Γ = hole ∧ b = cunit	P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ cunit = ↑Γ b ↔ Γ = hole ∧ b = cunit TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.cunit_eq	[168, 9]	[171, 7]	simp	P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_sunit	[173, 9]	[175, 40]	cases Γ <;> simp [FunLike.coe, subst]	P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.sunit_eq	[177, 9]	[180, 7]	rw [show (_ = _ ↔ _ = _) from ⟨Eq.symm, Eq.symm⟩]	P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ sunit = ↑Γ b ↔ Γ = hole ∧ b = sunit	P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ sunit = ↑Γ b ↔ Γ = hole ∧ b = sunit TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.sunit_eq	[177, 9]	[180, 7]	simp	P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_comma	[182, 1]	[188, 20]	cases Γ <;> aesop	P : Sort u_1 b Δ₁ Δ₂ : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = (Δ₁ ,ᵇ Δ₂) ↔ Γ = hole ∧ b = (Δ₁ ,ᵇ Δ₂) ∨ (∃ Γ', Γ = commaL Γ' Δ₂ ∧ ↑Γ' b = Δ₁) ∨ ∃ Γ', Γ = commaR Δ₁ Γ' ∧ ↑Γ' b = Δ₂	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b Δ₁ Δ₂ : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = (Δ₁ ,ᵇ Δ₂) ↔ Γ = hole ∧ b = (Δ₁ ,ᵇ Δ₂) ∨ (∃ Γ', Γ = commaL Γ' Δ₂ ∧ ↑Γ' b = Δ₁) ∨ ∃ Γ', Γ = commaR Δ₁ Γ' ∧ ↑Γ' b = Δ₂ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_semi	[190, 1]	[196, 20]	cases Γ <;> aesop	P : Sort u_1 b Δ₁ Δ₂ : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = (Δ₁ ;ᵇ Δ₂) ↔ Γ = hole ∧ b = (Δ₁ ;ᵇ Δ₂) ∨ (∃ Γ', Γ = semiL Γ' Δ₂ ∧ ↑Γ' b = Δ₁) ∨ ∃ Γ', Γ = semiR Δ₁ Γ' ∧ ↑Γ' b = Δ₂	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 b Δ₁ Δ₂ : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = (Δ₁ ;ᵇ Δ₂) ↔ Γ = hole ∧ b = (Δ₁ ;ᵇ Δ₂) ∨ (∃ Γ', Γ = semiL Γ' Δ₂ ∧ ↑Γ' b = Δ₁) ∨ ∃ Γ', Γ = semiR Δ₁ Γ' ∧ ↑Γ' b = Δ₂ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	intro h	P : Sort u_1 Γ Γ' : BunchWithHole P φ φ' : Bunch P ⊢ ↑Γ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	P : Sort u_1 Γ Γ' : BunchWithHole P φ φ' : Bunch P h : ↑Γ φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 Γ Γ' : BunchWithHole P φ φ' : Bunch P ⊢ ↑Γ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	induction Γ generalizing Γ'	P : Sort u_1 Γ Γ' : BunchWithHole P φ φ' : Bunch P h : ↑Γ φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	case hole P : Sort u_1 φ φ' : Bunch P Γ' : BunchWithHole P h : ↑hole φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case commaL P : Sort u_1 φ φ' : Bunch P l✝ : BunchWithHole P r✝ : Bunch P l_ih✝ : ∀ {Γ' : BunchWithHole P}, ↑l✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ l✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = l✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = l✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(commaL l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaL l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaL l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaL l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case commaR P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P r_ih✝ : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(commaR l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case semiL P : Sort u_1 φ φ' : Bunch P l✝ : BunchWithHole P r✝ : Bunch P l_ih✝ : ∀ {Γ' : BunchWithHole P}, ↑l✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ l✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = l✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = l✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(semiL l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiL l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiL l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiL l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case semiR P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P r_ih✝ : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(semiR l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 Γ Γ' : BunchWithHole P φ φ' : Bunch P h : ↑Γ φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	case hole => simp_all	P : Sort u_1 φ φ' : Bunch P Γ' : BunchWithHole P h : ↑hole φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' : Bunch P Γ' : BunchWithHole P h : ↑hole φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp_all	P : Sort u_1 φ φ' : Bunch P Γ' : BunchWithHole P h : ↑hole φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' : Bunch P Γ' : BunchWithHole P h : ↑hole φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp at h	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(semiR l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : (l✝ ;ᵇ ↑r✝ φ) = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(semiR l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	rw [eq_comm] at h	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : (l✝ ;ᵇ ↑r✝ φ) = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : (l✝ ;ᵇ ↑r✝ φ) = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	first \| rw [eq_comma] at h \| rw [eq_semi] at h	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	rcases h with (⟨rfl,rfl⟩\|⟨Γ'',rfl,h⟩\|⟨Γ'',rfl,h⟩)	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	case inl.intro P : Sort u_1 φ l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' (l✝ ;ᵇ ↑r✝ φ) → (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ (semiR l✝ r✝).comp Δ = hole) ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ hole.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = hole ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case inr.inl.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = l✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case inr.inr.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiR l✝ Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiR l✝ Γ'').comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiR l✝ Γ'' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	rw [eq_comma] at h	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ,ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ,ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = commaL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = commaR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ,ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	rw [eq_semi] at h	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp	case inl.intro P : Sort u_1 φ l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' (l✝ ;ᵇ ↑r✝ φ) → (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ (semiR l✝ r✝).comp Δ = hole) ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ hole.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = hole ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	no goals	Please generate a tactic in lean4 to solve the state. STATE: case inl.intro P : Sort u_1 φ l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' (l✝ ;ᵇ ↑r✝ φ) → (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ (semiR l✝ r✝).comp Δ = hole) ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ hole.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = hole ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiR l✝ Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiR l✝ Γ'').comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiR l✝ Γ'' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiR l✝ Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiR l✝ Γ'').comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiR l✝ Γ'' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	rw [eq_comm] at h	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑r✝ φ = ↑Γ'' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	rcases ih h with (h1\|h2\|⟨Δ,Δ',rfl,rfl,h3⟩) <;> clear ih h	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑r✝ φ = ↑Γ'' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	case inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h1 : ∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ case inr.inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h2 : ∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ case inr.inr.intro.intro.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ = ↑Δ_1 φ' ∧ (Δ' φ').comp Δ_1 = Δ φ) ∨ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑r✝ φ = ↑Γ'' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp [h1]	case inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h1 : ∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	no goals	Please generate a tactic in lean4 to solve the state. STATE: case inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h1 : ∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp [h2]	case inr.inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h2 : ∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	no goals	Please generate a tactic in lean4 to solve the state. STATE: case inr.inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h2 : ∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	apply Or.inr	case inr.inr.intro.intro.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ = ↑Δ_1 φ' ∧ (Δ' φ').comp Δ_1 = Δ φ) ∨ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ = ↑Δ_1 φ' ∧ (Δ' φ').comp Δ_1 = Δ φ) ∨ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	apply Or.inr	case inr.inr.intro.intro.intro.intro.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	iterate 2 ( first \| refine ⟨(fun x => commaL _ _),rfl,?_⟩ \| refine ⟨(fun x => commaR _ _),rfl,?_⟩ \| refine ⟨(fun x => semiL _ _),rfl,?_⟩ \| refine ⟨(fun x => semiR _ _),rfl,?_⟩ )	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	intro ψ ψ'	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ψ ψ' : Bunch P ⊢ ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp [h3]	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ψ ψ' : Bunch P ⊢ ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ	no goals	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ψ ψ' : Bunch P ⊢ ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	( first \| refine ⟨(fun x => commaL _ _),rfl,?_⟩ \| refine ⟨(fun x => commaR _ _),rfl,?_⟩ \| refine ⟨(fun x => semiL _ _),rfl,?_⟩ \| refine ⟨(fun x => semiR _ _),rfl,?_⟩ )	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	first \| refine ⟨(fun x => commaL _ _),rfl,?_⟩ \| refine ⟨(fun x => commaR _ _),rfl,?_⟩ \| refine ⟨(fun x => semiL _ _),rfl,?_⟩ \| refine ⟨(fun x => semiR _ _),rfl,?_⟩	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	refine ⟨(fun x => commaL _ _),rfl,?_⟩	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = commaL (Δ' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL (Δ x) r✝) ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL (Δ x) r✝) ψ) ψ' = ↑((fun x => commaL (Δ' x) r✝) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = commaL (Δ' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL (Δ x) r✝) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	refine ⟨(fun x => commaR _ _),rfl,?_⟩	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = commaR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Δ x)) ψ) ψ' = ↑((fun x => commaR l✝ (Δ' x)) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = commaR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	refine ⟨(fun x => semiL _ _),rfl,?_⟩	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiL (Δ' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL (Δ x) r✝) ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL (Δ x) r✝) ψ) ψ' = ↑((fun x => semiL (Δ' x) r✝) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiL (Δ' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL (Δ x) r✝) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	refine ⟨(fun x => semiR _ _),rfl,?_⟩	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ	case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	cases h	P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = l✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR (↑Γ'' φ') r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR (↑Γ'' φ') r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = l✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR (↑Γ'' φ') r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR (↑Γ'' φ') r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR (↑Γ'' φ') r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR (↑Γ'' φ') r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	iterate 2 ( first \| refine ⟨(fun x => commaL _ _),rfl,?_⟩ \| refine ⟨(fun x => commaR _ _),rfl,?_⟩ \| refine ⟨(fun x => semiL _ _),rfl,?_⟩ \| refine ⟨(fun x => semiR _ _),rfl,?_⟩ )	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	intro ψ ψ'	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ψ ψ' : Bunch P ⊢ ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	simp	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ψ ψ' : Bunch P ⊢ ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ	no goals	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ψ ψ' : Bunch P ⊢ ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	( first \| refine ⟨(fun x => commaL _ _),rfl,?_⟩ \| refine ⟨(fun x => commaR _ _),rfl,?_⟩ \| refine ⟨(fun x => semiL _ _),rfl,?_⟩ \| refine ⟨(fun x => semiR _ _),rfl,?_⟩ )	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	first \| refine ⟨(fun x => commaL _ _),rfl,?_⟩ \| refine ⟨(fun x => commaR _ _),rfl,?_⟩ \| refine ⟨(fun x => semiL _ _),rfl,?_⟩ \| refine ⟨(fun x => semiR _ _),rfl,?_⟩	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	refine ⟨(fun x => commaL _ _),rfl,?_⟩	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = commaL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = commaL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	refine ⟨(fun x => commaR _ _),rfl,?_⟩	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => commaR (↑Γ'' x) r✝) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	refine ⟨(fun x => semiL _ _),rfl,?_⟩	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.eq_inv	[198, 1]	[239, 13]	refine ⟨(fun x => semiR _ _),rfl,?_⟩	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ	case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ	Please generate a tactic in lean4 to solve the state. STATE: case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.idem	[241, 9]	[243, 21]	simp [FunLike.coe]	P : Sort u_1 Γ : BunchWithHole P b : Bunch P ⊢ ↑Γ b = b ↔ Γ = hole	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 Γ : BunchWithHole P b : Bunch P ⊢ ↑Γ b = b ↔ Γ = hole TACTIC:
https://github.com/JamesGallicchio/brunched-invitations.git	3082c5ae68d2022b1439310f315a0038dae24e0c	BunchImpl/Bunch.lean	BunchImpl.BunchWithHole.idem'	[245, 9]	[247, 21]	simp [FunLike.coe]	P : Sort u_1 Γ : BunchWithHole P b : Bunch P ⊢ b = ↑Γ b ↔ Γ = hole	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Sort u_1 Γ : BunchWithHole P b : Bunch P ⊢ b = ↑Γ b ↔ Γ = hole TACTIC: