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|---|---|---|---|---|---|---|---|---|---|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_assoc | [134, 1] | [144, 4] | intros a b c | β’ β (a b c : Rotation), a + b + c = a + (b + c) | a b c : Rotation
β’ a + b + c = a + (b + c) | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (a b c : Rotation), a + b + c = a + (b + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_assoc | [134, 1] | [144, 4] | cases a | a b c : Rotation
β’ a + b + c = a + (b + c) | case r0
b c : Rotation
β’ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
β’ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c) | Please generate a tactic in lean4 to solve the state.
STATE:
a b c : Rotation
β’ a + b + c = a + (b + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_assoc | [134, 1] | [144, 4] | repeat {
cases b
repeat {
cases c
repeat { rfl }
}
} | case r0
b c : Rotation
β’ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
β’ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r0
b c : Rotation
β’ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
β’ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_assoc | [134, 1] | [144, 4] | cases b | case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c) | case r240.r0
c : Rotation
β’ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
β’ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c) | Please generate a tactic in lean4 to solve the state.
STATE:
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_assoc | [134, 1] | [144, 4] | repeat {
cases c
repeat { rfl }
} | case r240.r0
c : Rotation
β’ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
β’ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r240.r0
c : Rotation
β’ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
β’ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_assoc | [134, 1] | [144, 4] | cases c | case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c) | case r240.r240.r0
β’ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
β’ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240) | Please generate a tactic in lean4 to solve the state.
STATE:
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_assoc | [134, 1] | [144, 4] | repeat { rfl } | case r240.r240.r0
β’ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
β’ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r240.r240.r0
β’ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
β’ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_assoc | [134, 1] | [144, 4] | rfl | case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_zero_add | [157, 1] | [161, 17] | intro a | β’ β (a : Rotation), 0 + a = a | a : Rotation
β’ 0 + a = a | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (a : Rotation), 0 + a = a
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_zero_add | [157, 1] | [161, 17] | cases a | a : Rotation
β’ 0 + a = a | case r0
β’ 0 + r0 = r0
case r120
β’ 0 + r120 = r120
case r240
β’ 0 + r240 = r240 | Please generate a tactic in lean4 to solve the state.
STATE:
a : Rotation
β’ 0 + a = a
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_zero_add | [157, 1] | [161, 17] | repeat { rfl } | case r0
β’ 0 + r0 = r0
case r120
β’ 0 + r120 = r120
case r240
β’ 0 + r240 = r240 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r0
β’ 0 + r0 = r0
case r120
β’ 0 + r120 = r120
case r240
β’ 0 + r240 = r240
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_zero_add | [157, 1] | [161, 17] | rfl | case r240
β’ 0 + r240 = r240 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r240
β’ 0 + r240 = r240
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_zero | [163, 1] | [167, 17] | intro a | β’ β (a : Rotation), a + 0 = a | a : Rotation
β’ a + 0 = a | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (a : Rotation), a + 0 = a
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_zero | [163, 1] | [167, 17] | cases a | a : Rotation
β’ a + 0 = a | case r0
β’ r0 + 0 = r0
case r120
β’ r120 + 0 = r120
case r240
β’ r240 + 0 = r240 | Please generate a tactic in lean4 to solve the state.
STATE:
a : Rotation
β’ a + 0 = a
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_zero | [163, 1] | [167, 17] | repeat { rfl } | case r0
β’ r0 + 0 = r0
case r120
β’ r120 + 0 = r120
case r240
β’ r240 + 0 = r240 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r0
β’ r0 + 0 = r0
case r120
β’ r120 + 0 = r120
case r240
β’ r240 + 0 = r240
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_zero | [163, 1] | [167, 17] | rfl | case r240
β’ r240 + 0 = r240 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r240
β’ r240 + 0 = r240
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_zero_vadd | [219, 1] | [223, 17] | intro p | β’ β (p : State), 0 +α΅₯ p = p | p : State
β’ 0 +α΅₯ p = p | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (p : State), 0 +α΅₯ p = p
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_zero_vadd | [219, 1] | [223, 17] | cases p | p : State
β’ 0 +α΅₯ p = p | case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ | Please generate a tactic in lean4 to solve the state.
STATE:
p : State
β’ 0 +α΅₯ p = p
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_zero_vadd | [219, 1] | [223, 17] | repeat { rfl } | case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_zero_vadd | [219, 1] | [223, 17] | rfl | case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_vadd | [225, 1] | [235, 4] | intros gβ gβ p | β’ β (gβ gβ : Rotation) (p : State), gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p) | gβ gβ : Rotation
p : State
β’ gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p) | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (gβ gβ : Rotation) (p : State), gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_vadd | [225, 1] | [235, 4] | cases gβ | gβ gβ : Rotation
p : State
β’ gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p) | case r0
gβ : Rotation
p : State
β’ r0 + gβ +α΅₯ p = r0 +α΅₯ (gβ +α΅₯ p)
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
case r240
gβ : Rotation
p : State
β’ r240 + gβ +α΅₯ p = r240 +α΅₯ (gβ +α΅₯ p) | Please generate a tactic in lean4 to solve the state.
STATE:
gβ gβ : Rotation
p : State
β’ gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_vadd | [225, 1] | [235, 4] | repeat {
cases gβ
repeat {
cases p
repeat rfl
}
} | case r0
gβ : Rotation
p : State
β’ r0 + gβ +α΅₯ p = r0 +α΅₯ (gβ +α΅₯ p)
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
case r240
gβ : Rotation
p : State
β’ r240 + gβ +α΅₯ p = r240 +α΅₯ (gβ +α΅₯ p) | case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
case r240
gβ : Rotation
p : State
β’ r240 + gβ +α΅₯ p = r240 +α΅₯ (gβ +α΅₯ p) | Please generate a tactic in lean4 to solve the state.
STATE:
case r0
gβ : Rotation
p : State
β’ r0 + gβ +α΅₯ p = r0 +α΅₯ (gβ +α΅₯ p)
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
case r240
gβ : Rotation
p : State
β’ r240 + gβ +α΅₯ p = r240 +α΅₯ (gβ +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_vadd | [225, 1] | [235, 4] | cases gβ | case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p) | case r120.r0
p : State
β’ r120 + r0 +α΅₯ p = r120 +α΅₯ (r0 +α΅₯ p)
case r120.r120
p : State
β’ r120 + r120 +α΅₯ p = r120 +α΅₯ (r120 +α΅₯ p)
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p) | Please generate a tactic in lean4 to solve the state.
STATE:
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_vadd | [225, 1] | [235, 4] | repeat {
cases p
repeat rfl
} | case r120.r0
p : State
β’ r120 + r0 +α΅₯ p = r120 +α΅₯ (r0 +α΅₯ p)
case r120.r120
p : State
β’ r120 + r120 +α΅₯ p = r120 +α΅₯ (r120 +α΅₯ p)
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p) | case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p) | Please generate a tactic in lean4 to solve the state.
STATE:
case r120.r0
p : State
β’ r120 + r0 +α΅₯ p = r120 +α΅₯ (r0 +α΅₯ p)
case r120.r120
p : State
β’ r120 + r120 +α΅₯ p = r120 +α΅₯ (r120 +α΅₯ p)
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_vadd | [225, 1] | [235, 4] | cases p | case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p) | case r120.r240.heading
hβ : K
unitβ : β
β’ r120 + r240 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r240 +α΅₯ heading hβ unitβ) | Please generate a tactic in lean4 to solve the state.
STATE:
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_vadd | [225, 1] | [235, 4] | repeat rfl | case r120.r120.heading
hβ : K
unitβ : β
β’ r120 + r120 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r120 +α΅₯ heading hβ unitβ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r120.r120.heading
hβ : K
unitβ : β
β’ r120 + r120 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r120 +α΅₯ heading hβ unitβ)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_vadd | [225, 1] | [235, 4] | rfl | case r120.r120.heading
hβ : K
unitβ : β
β’ r120 + r120 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r120 +α΅₯ heading hβ unitβ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r120.r120.heading
hβ : K
unitβ : β
β’ r120 + r120 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r120 +α΅₯ heading hβ unitβ)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_neg_left | [349, 1] | [353, 17] | intro a | β’ β (a : Rotation), -a + a = 0 | a : Rotation
β’ -a + a = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (a : Rotation), -a + a = 0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_neg_left | [349, 1] | [353, 17] | cases a | a : Rotation
β’ -a + a = 0 | case r0
β’ -r0 + r0 = 0
case r120
β’ -r120 + r120 = 0
case r240
β’ -r240 + r240 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
a : Rotation
β’ -a + a = 0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_neg_left | [349, 1] | [353, 17] | repeat { rfl } | case r0
β’ -r0 + r0 = 0
case r120
β’ -r120 + r120 = 0
case r240
β’ -r240 + r240 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r0
β’ -r0 + r0 = 0
case r120
β’ -r120 + r120 = 0
case r240
β’ -r240 + r240 = 0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_add_neg_left | [349, 1] | [353, 17] | rfl | case r240
β’ -r240 + r240 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case r240
β’ -r240 + r240 = 0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_state_vsub_vadd' | [405, 1] | [412, 4] | intro p1 p2 | β’ β (p1 p2 : State), p1 -α΅₯ p2 +α΅₯ p2 = p1 | p1 p2 : State
β’ p1 -α΅₯ p2 +α΅₯ p2 = p1 | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (p1 p2 : State), p1 -α΅₯ p2 +α΅₯ p2 = p1
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_state_vsub_vadd' | [405, 1] | [412, 4] | cases p1 | p1 p2 : State
β’ p1 -α΅₯ p2 +α΅₯ p2 = p1 | case heading
p2 : State
hβ : K
unitβ : β
β’ heading hβ unitβ -α΅₯ p2 +α΅₯ p2 = heading hβ unitβ | Please generate a tactic in lean4 to solve the state.
STATE:
p1 p2 : State
β’ p1 -α΅₯ p2 +α΅₯ p2 = p1
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_state_vsub_vadd' | [405, 1] | [412, 4] | cases p2 | case heading
p2 : State
hβ : K
unitβ : β
β’ heading hβ unitβ -α΅₯ p2 +α΅₯ p2 = heading hβ unitβ | case heading.heading
hβΒΉ : K
unitβΒΉ : β
hβ : K
unitβ : β
β’ heading hβΒΉ unitβΒΉ -α΅₯ heading hβ unitβ +α΅₯ heading hβ unitβ = heading hβΒΉ unitβΒΉ | Please generate a tactic in lean4 to solve the state.
STATE:
case heading
p2 : State
hβ : K
unitβ : β
β’ heading hβ unitβ -α΅₯ p2 +α΅₯ p2 = heading hβ unitβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_state_vadd_vsub' | [414, 1] | [421, 4] | intros g p | β’ β (g : Rotation) (p : State), g +α΅₯ p -α΅₯ p = g | g : Rotation
p : State
β’ g +α΅₯ p -α΅₯ p = g | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (g : Rotation) (p : State), g +α΅₯ p -α΅₯ p = g
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_state_vadd_vsub' | [414, 1] | [421, 4] | cases g | g : Rotation
p : State
β’ g +α΅₯ p -α΅₯ p = g | case r0
p : State
β’ r0 +α΅₯ p -α΅₯ p = r0
case r120
p : State
β’ r120 +α΅₯ p -α΅₯ p = r120
case r240
p : State
β’ r240 +α΅₯ p -α΅₯ p = r240 | Please generate a tactic in lean4 to solve the state.
STATE:
g : Rotation
p : State
β’ g +α΅₯ p -α΅₯ p = g
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/vector_spaces.lean | rot_state_vadd_vsub' | [414, 1] | [421, 4] | cases p | case r0
p : State
β’ r0 +α΅₯ p -α΅₯ p = r0 | case r0.heading
hβ : K
unitβ : β
β’ r0 +α΅₯ heading hβ unitβ -α΅₯ heading hβ unitβ = r0 | Please generate a tactic in lean4 to solve the state.
STATE:
case r0
p : State
β’ r0 +α΅₯ p -α΅₯ p = r0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_refl | [68, 1] | [71, 12] | unfold Reflexive | β’ Reflexive Eq | β’ β (x : β), x = x | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Reflexive Eq
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_refl | [68, 1] | [71, 12] | intro x | β’ β (x : β), x = x | x : β
β’ x = x | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (x : β), x = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_refl | [68, 1] | [71, 12] | exact rfl | x : β
β’ x = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : β
β’ x = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_symm | [73, 1] | [77, 11] | unfold Symmetric | β’ Symmetric Eq | β’ β β¦x y : ββ¦, x = y β y = x | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Symmetric Eq
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_symm | [73, 1] | [77, 11] | intro x y | β’ β β¦x y : ββ¦, x = y β y = x | x y : β
β’ x = y β y = x | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β β¦x y : ββ¦, x = y β y = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_symm | [73, 1] | [77, 11] | intro hxy | x y : β
β’ x = y β y = x | x y : β
hxy : x = y
β’ y = x | Please generate a tactic in lean4 to solve the state.
STATE:
x y : β
β’ x = y β y = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_symm | [73, 1] | [77, 11] | rw [hxy] | x y : β
hxy : x = y
β’ y = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : β
hxy : x = y
β’ y = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_trans | [82, 1] | [87, 9] | unfold Transitive | β’ Transitive Eq | β’ β β¦x y z : ββ¦, x = y β y = z β x = z | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Transitive Eq
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_trans | [82, 1] | [87, 9] | intros x y z | β’ β β¦x y z : ββ¦, x = y β y = z β x = z | x y z : β
β’ x = y β y = z β x = z | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β β¦x y z : ββ¦, x = y β y = z β x = z
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_trans | [82, 1] | [87, 9] | intros hxy hyz | x y z : β
β’ x = y β y = z β x = z | x y z : β
hxy : x = y
hyz : y = z
β’ x = z | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : β
β’ x = y β y = z β x = z
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_trans | [82, 1] | [87, 9] | rw [hxy] | x y z : β
hxy : x = y
hyz : y = z
β’ x = z | x y z : β
hxy : x = y
hyz : y = z
β’ y = z | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : β
hxy : x = y
hyz : y = z
β’ x = z
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | eq_nat_is_trans | [82, 1] | [87, 9] | rw [hyz] | x y z : β
hxy : x = y
hyz : y = z
β’ y = z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : β
hxy : x = y
hyz : y = z
β’ y = z
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv' | [99, 1] | [102, 31] | intro n | β’ β (n : β), Equivalence (cong_mod_n n) | n : β
β’ Equivalence (cong_mod_n n) | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Equivalence (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_rfl | [106, 1] | [111, 12] | intro n | β’ β (n : β), Reflexive (cong_mod_n n) | n : β
β’ Reflexive (cong_mod_n n) | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Reflexive (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_rfl | [106, 1] | [111, 12] | unfold cong_mod_n | n : β
β’ Reflexive (cong_mod_n n) | n : β
β’ Reflexive fun a b => a % n = b % n | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Reflexive (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_rfl | [106, 1] | [111, 12] | unfold Reflexive | n : β
β’ Reflexive fun a b => a % n = b % n | n : β
β’ β (x : β), (fun a b => a % n = b % n) x x | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Reflexive fun a b => a % n = b % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_rfl | [106, 1] | [111, 12] | intro a | n : β
β’ β (x : β), (fun a b => a % n = b % n) x x | n a : β
β’ a % n = a % n | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β (x : β), (fun a b => a % n = b % n) x x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_rfl | [106, 1] | [111, 12] | exact rfl | n a : β
β’ a % n = a % n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n a : β
β’ a % n = a % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_symm | [113, 1] | [120, 11] | intro n | β’ β (n : β), Symmetric (cong_mod_n n) | n : β
β’ Symmetric (cong_mod_n n) | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Symmetric (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_symm | [113, 1] | [120, 11] | unfold Symmetric | n : β
β’ Symmetric (cong_mod_n n) | n : β
β’ β β¦x y : ββ¦, cong_mod_n n x y β cong_mod_n n y x | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Symmetric (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_symm | [113, 1] | [120, 11] | intros x y | n : β
β’ β β¦x y : ββ¦, cong_mod_n n x y β cong_mod_n n y x | n x y : β
β’ cong_mod_n n x y β cong_mod_n n y x | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β β¦x y : ββ¦, cong_mod_n n x y β cong_mod_n n y x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_symm | [113, 1] | [120, 11] | intro hxy | n x y : β
β’ cong_mod_n n x y β cong_mod_n n y x | n x y : β
hxy : cong_mod_n n x y
β’ cong_mod_n n y x | Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
β’ cong_mod_n n x y β cong_mod_n n y x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_symm | [113, 1] | [120, 11] | unfold cong_mod_n | n x y : β
hxy : cong_mod_n n x y
β’ cong_mod_n n y x | n x y : β
hxy : cong_mod_n n x y
β’ y % n = x % n | Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
hxy : cong_mod_n n x y
β’ cong_mod_n n y x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_symm | [113, 1] | [120, 11] | unfold cong_mod_n at hxy | n x y : β
hxy : cong_mod_n n x y
β’ y % n = x % n | n x y : β
hxy : x % n = y % n
β’ y % n = x % n | Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
hxy : cong_mod_n n x y
β’ y % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_symm | [113, 1] | [120, 11] | rw [hxy] | n x y : β
hxy : x % n = y % n
β’ y % n = x % n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
hxy : x % n = y % n
β’ y % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_trans | [122, 1] | [126, 16] | intro n a b c hab hbc | β’ β (n : β), Transitive (cong_mod_n n) | n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ cong_mod_n n a c | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Transitive (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_trans | [122, 1] | [126, 16] | unfold cong_mod_n | n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ cong_mod_n n a c | n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ a % n = c % n | Please generate a tactic in lean4 to solve the state.
STATE:
n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ cong_mod_n n a c
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_trans | [122, 1] | [126, 16] | unfold cong_mod_n at hab hbc | n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ a % n = c % n | n a b c : β
hab : a % n = b % n
hbc : b % n = c % n
β’ a % n = c % n | Please generate a tactic in lean4 to solve the state.
STATE:
n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ a % n = c % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_trans | [122, 1] | [126, 16] | rw [hab, hbc] | n a b c : β
hab : a % n = b % n
hbc : b % n = c % n
β’ a % n = c % n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n a b c : β
hab : a % n = b % n
hbc : b % n = c % n
β’ a % n = c % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | intro n | β’ β (n : β), Equivalence (cong_mod_n n) | n : β
β’ Equivalence (cong_mod_n n) | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Equivalence (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | unfold cong_mod_n | n : β
β’ Equivalence (cong_mod_n n) | n : β
β’ Equivalence fun a b => a % n = b % n | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Equivalence (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | exact Equivalence.mk
(by intro x; rfl)
(by intros x y h; rw [h])
(by intros x y z hxy hyz; rw [hxy, hyz]) | n : β
β’ Equivalence fun a b => a % n = b % n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Equivalence fun a b => a % n = b % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | intro x | n : β
β’ β (x : β), x % n = x % n | n x : β
β’ x % n = x % n | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β (x : β), x % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | rfl | n x : β
β’ x % n = x % n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n x : β
β’ x % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | intros x y h | n : β
β’ β {x y : β}, x % n = y % n β y % n = x % n | n x y : β
h : x % n = y % n
β’ y % n = x % n | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β {x y : β}, x % n = y % n β y % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | rw [h] | n x y : β
h : x % n = y % n
β’ y % n = x % n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
h : x % n = y % n
β’ y % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | intros x y z hxy hyz | n : β
β’ β {x y z : β}, x % n = y % n β y % n = z % n β x % n = z % n | n x y z : β
hxy : x % n = y % n
hyz : y % n = z % n
β’ x % n = z % n | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β {x y z : β}, x % n = y % n β y % n = z % n β x % n = z % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | cong_mod_n_equiv | [128, 1] | [135, 47] | rw [hxy, hyz] | n x y z : β
hxy : x % n = y % n
hyz : y % n = z % n
β’ x % n = z % n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n x y z : β
hxy : x % n = y % n
hyz : y % n = z % n
β’ x % n = z % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | succ_inj | [189, 1] | [193, 13] | unfold Injective | β’ Injective fun n => n + 1 | β’ β β¦aβ aβ : ββ¦, (fun n => n + 1) aβ = (fun n => n + 1) aβ β aβ = aβ | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Injective fun n => n + 1
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | succ_inj | [189, 1] | [193, 13] | intros a1 a2 h | β’ β β¦aβ aβ : ββ¦, (fun n => n + 1) aβ = (fun n => n + 1) aβ β aβ = aβ | a1 a2 : β
h : (fun n => n + 1) a1 = (fun n => n + 1) a2
β’ a1 = a2 | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β β¦aβ aβ : ββ¦, (fun n => n + 1) aβ = (fun n => n + 1) aβ β aβ = aβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | succ_inj | [189, 1] | [193, 13] | simp [Nat.add] at h | a1 a2 : β
h : (fun n => n + 1) a1 = (fun n => n + 1) a2
β’ a1 = a2 | a1 a2 : β
h : a1 = a2
β’ a1 = a2 | Please generate a tactic in lean4 to solve the state.
STATE:
a1 a2 : β
h : (fun n => n + 1) a1 = (fun n => n + 1) a2
β’ a1 = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | succ_inj | [189, 1] | [193, 13] | assumption | a1 a2 : β
h : a1 = a2
β’ a1 = a2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a1 a2 : β
h : a1 = a2
β’ a1 = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | not_succ_surj | [196, 1] | [200, 27] | unfold Surjective | β’ Β¬Surjective fun n => n + 1 | β’ Β¬β (b : β), β a, (fun n => n + 1) a = b | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Β¬Surjective fun n => n + 1
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | not_succ_surj | [196, 1] | [200, 27] | intro h | β’ Β¬β (b : β), β a, (fun n => n + 1) a = b | h : β (b : β), β a, (fun n => n + 1) a = b
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Β¬β (b : β), β a, (fun n => n + 1) a = b
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | not_succ_surj | [196, 1] | [200, 27] | let contra := h 0 | h : β (b : β), β a, (fun n => n + 1) a = b
β’ False | h : β (b : β), β a, (fun n => n + 1) a = b
contra : β a, (fun n => n + 1) a = 0 := h 0
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
h : β (b : β), β a, (fun n => n + 1) a = b
β’ False
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | not_succ_surj | [196, 1] | [200, 27] | simp [Nat.add] at contra | h : β (b : β), β a, (fun n => n + 1) a = b
contra : β a, (fun n => n + 1) a = 0 := h 0
β’ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
h : β (b : β), β a, (fun n => n + 1) a = b
contra : β a, (fun n => n + 1) a = 0 := h 0
β’ False
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | unfold Injective | β’ Injective Bool.not | β’ β β¦aβ aβ : Boolβ¦, Bool.not aβ = Bool.not aβ β aβ = aβ | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Injective Bool.not
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | intros a1 a2 h | β’ β β¦aβ aβ : Boolβ¦, Bool.not aβ = Bool.not aβ β aβ = aβ | a1 a2 : Bool
h : Bool.not a1 = Bool.not a2
β’ a1 = a2 | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β β¦aβ aβ : Boolβ¦, Bool.not aβ = Bool.not aβ β aβ = aβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | cases a1 with
| true =>
cases a2 with
| true => rfl
| false => nomatch h
| false =>
cases a2 with
| true => nomatch h
| false => rfl | a1 a2 : Bool
h : Bool.not a1 = Bool.not a2
β’ a1 = a2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a1 a2 : Bool
h : Bool.not a1 = Bool.not a2
β’ a1 = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | cases a2 with
| true => rfl
| false => nomatch h | case true
a2 : Bool
h : Bool.not true = Bool.not a2
β’ true = a2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case true
a2 : Bool
h : Bool.not true = Bool.not a2
β’ true = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | rfl | case true.true
h : Bool.not true = Bool.not true
β’ true = true | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case true.true
h : Bool.not true = Bool.not true
β’ true = true
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | nomatch h | case true.false
h : Bool.not true = Bool.not false
β’ true = false | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case true.false
h : Bool.not true = Bool.not false
β’ true = false
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | cases a2 with
| true => nomatch h
| false => rfl | case false
a2 : Bool
h : Bool.not false = Bool.not a2
β’ false = a2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case false
a2 : Bool
h : Bool.not false = Bool.not a2
β’ false = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | nomatch h | case false.true
h : Bool.not false = Bool.not true
β’ false = true | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case false.true
h : Bool.not false = Bool.not true
β’ false = true
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | inj_not | [204, 1] | [215, 25] | rfl | case false.false
h : Bool.not false = Bool.not false
β’ false = false | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case false.false
h : Bool.not false = Bool.not false
β’ false = false
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | surj_not | [217, 1] | [222, 33] | unfold Surjective | β’ Surjective Bool.not | β’ β (b : Bool), β a, Bool.not a = b | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Surjective Bool.not
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | surj_not | [217, 1] | [222, 33] | intro b | β’ β (b : Bool), β a, Bool.not a = b | b : Bool
β’ β a, Bool.not a = b | Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (b : Bool), β a, Bool.not a = b
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | surj_not | [217, 1] | [222, 33] | cases b with
| true => exact β¨ false, rfl β©
| false => exact β¨ true, rfl β© | b : Bool
β’ β a, Bool.not a = b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
β’ β a, Bool.not a = b
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | surj_not | [217, 1] | [222, 33] | exact β¨ false, rfl β© | case true
β’ β a, Bool.not a = true | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case true
β’ β a, Bool.not a = true
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | surj_not | [217, 1] | [222, 33] | exact β¨ true, rfl β© | case false
β’ β a, Bool.not a = false | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case false
β’ β a, Bool.not a = false
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | not_bij | [224, 1] | [226, 30] | unfold Bijective | β’ Bijective Bool.not | β’ Injective Bool.not β§ Surjective Bool.not | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Bijective Bool.not
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git | c2da7c4a6be769c6fca375a54e8c1fa31ba2854b | Instructor/Lectures/grad/sets_relations.lean | not_bij | [224, 1] | [226, 30] | exact β¨ inj_not, surj_not β© | β’ Injective Bool.not β§ Surjective Bool.not | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Injective Bool.not β§ Surjective Bool.not
TACTIC:
|
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