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
|
|---|---|---|---|---|---|---|---|---|
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.RTC_SmallStep_of_BigStep | [688, 1] | [728, 17] | apply SmallStep.seq_skip | case while_true.hbc.hbc.hbc.hab
Ss : Stmt × State
t✝ : State
B : State → Prop
S : Stmt
s t u : State
hB : B s
hS : (S, s) ⟹ t
hw : (Stmt.whileDo B S, t) ⟹ u
ihS : RTC SmallStep (S, s) (Stmt.skip, t)
ihw : RTC SmallStep (Stmt.whileDo B S, t) (Stmt.skip, u)
⊢ (Stmt.skip; Stmt.whileDo B S, t) ⇒ ?while_true.hbc.hbc.hbc.b
case while_true.hbc.hbc.hbc.hbc
Ss : Stmt × State
t✝ : State
B : State → Prop
S : Stmt
s t u : State
hB : B s
hS : (S, s) ⟹ t
hw : (Stmt.whileDo B S, t) ⟹ u
ihS : RTC SmallStep (S, s) (Stmt.skip, t)
ihw : RTC SmallStep (Stmt.whileDo B S, t) (Stmt.skip, u)
⊢ RTC SmallStep ?while_true.hbc.hbc.hbc.b (Stmt.skip, u)
case while_true.hbc.hbc.hbc.b
Ss : Stmt × State
t✝ : State
B : State → Prop
S : Stmt
s t u : State
hB : B s
hS : (S, s) ⟹ t
hw : (Stmt.whileDo B S, t) ⟹ u
ihS : RTC SmallStep (S, s) (Stmt.skip, t)
ihw : RTC SmallStep (Stmt.whileDo B S, t) (Stmt.skip, u)
⊢ Stmt × State | case while_true.hbc.hbc.hbc.hbc
Ss : Stmt × State
t✝ : State
B : State → Prop
S : Stmt
s t u : State
hB : B s
hS : (S, s) ⟹ t
hw : (Stmt.whileDo B S, t) ⟹ u
ihS : RTC SmallStep (S, s) (Stmt.skip, t)
ihw : RTC SmallStep (Stmt.whileDo B S, t) (Stmt.skip, u)
⊢ RTC SmallStep (Stmt.whileDo B S, t) (Stmt.skip, u) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.RTC_SmallStep_of_BigStep | [688, 1] | [728, 17] | assumption | case while_true.hbc.hbc.hbc.hbc
Ss : Stmt × State
t✝ : State
B : State → Prop
S : Stmt
s t u : State
hB : B s
hS : (S, s) ⟹ t
hw : (Stmt.whileDo B S, t) ⟹ u
ihS : RTC SmallStep (S, s) (Stmt.skip, t)
ihw : RTC SmallStep (Stmt.whileDo B S, t) (Stmt.skip, u)
⊢ RTC SmallStep (Stmt.whileDo B S, t) (Stmt.skip, u) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.RTC_SmallStep_of_BigStep | [688, 1] | [728, 17] | apply RTC.tail | case while_false
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ RTC SmallStep (Stmt.whileDo B S, s) (Stmt.skip, s) | case while_false.hab
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ RTC SmallStep (Stmt.whileDo B S, s) ?while_false.b
case while_false.hbc
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ ?while_false.b ⇒ (Stmt.skip, s)
case while_false.b
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ Stmt × State |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.RTC_SmallStep_of_BigStep | [688, 1] | [728, 17] | apply RTC.single | case while_false.hab
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ RTC SmallStep (Stmt.whileDo B S, s) ?while_false.b
case while_false.hbc
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ ?while_false.b ⇒ (Stmt.skip, s)
case while_false.b
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ Stmt × State | case while_false.hab.hab
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ (Stmt.whileDo B S, s) ⇒ ?while_false.b
case while_false.hbc
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ ?while_false.b ⇒ (Stmt.skip, s)
case while_false.b
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ Stmt × State |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.RTC_SmallStep_of_BigStep | [688, 1] | [728, 17] | apply SmallStep.whileDo | case while_false.hab.hab
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ (Stmt.whileDo B S, s) ⇒ ?while_false.b
case while_false.hbc
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ ?while_false.b ⇒ (Stmt.skip, s)
case while_false.b
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ Stmt × State | case while_false.hbc
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⇒ (Stmt.skip, s) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.RTC_SmallStep_of_BigStep | [688, 1] | [728, 17] | apply SmallStep.if_false | case while_false.hbc
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⇒ (Stmt.skip, s) | case while_false.hbc.hcond
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ ¬B s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.RTC_SmallStep_of_BigStep | [688, 1] | [728, 17] | assumption | case while_false.hbc.hcond
Ss : Stmt × State
t : State
B : State → Prop
S : Stmt
s : State
hB : ¬B s
⊢ ¬B s | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_SmallStep_of_BigStep | [730, 1] | [740, 42] | induction h₁ generalizing s₂ with
| assign x a s => simp
| seq_step S S' T s s' hS ih => aesop
| seq_skip T s => simp
| if_true B S T s hB => aesop
| if_false B S T s hB => aesop
| whileDo B S s => aesop | Ss₀ Ss₁ : Stmt × State
s₂ : State
h₁ : Ss₀ ⇒ Ss₁
⊢ Ss₁ ⟹ s₂ → Ss₀ ⟹ s₂ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_SmallStep_of_BigStep | [730, 1] | [740, 42] | simp | case assign
Ss₀ Ss₁ : Stmt × State
x : String
a : State → ℕ
s s₂ : State
⊢ (Stmt.skip, State.update x (a s) s) ⟹ s₂ → (Stmt.assign x a, s) ⟹ s₂ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_SmallStep_of_BigStep | [730, 1] | [740, 42] | aesop | case seq_step
Ss₀ Ss₁ : Stmt × State
S S' T : Stmt
s s' : State
hS : (S, s) ⇒ (S', s')
ih : ∀ {s₂ : State}, (S', s') ⟹ s₂ → (S, s) ⟹ s₂
s₂ : State
⊢ (S'; T, s') ⟹ s₂ → (S; T, s) ⟹ s₂ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_SmallStep_of_BigStep | [730, 1] | [740, 42] | simp | case seq_skip
Ss₀ Ss₁ : Stmt × State
T : Stmt
s s₂ : State
⊢ (T, s) ⟹ s₂ → (Stmt.skip; T, s) ⟹ s₂ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_SmallStep_of_BigStep | [730, 1] | [740, 42] | aesop | case if_true
Ss₀ Ss₁ : Stmt × State
B : State → Prop
S T : Stmt
s : State
hB : B s
s₂ : State
⊢ (S, s) ⟹ s₂ → (Stmt.ifThenElse B S T, s) ⟹ s₂ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_SmallStep_of_BigStep | [730, 1] | [740, 42] | aesop | case if_false
Ss₀ Ss₁ : Stmt × State
B : State → Prop
S T : Stmt
s : State
hB : ¬B s
s₂ : State
⊢ (T, s) ⟹ s₂ → (Stmt.ifThenElse B S T, s) ⟹ s₂ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_SmallStep_of_BigStep | [730, 1] | [740, 42] | aesop | case whileDo
Ss₀ Ss₁ : Stmt × State
B : State → Prop
S : Stmt
s s₂ : State
⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ s₂ → (Stmt.whileDo B S, s) ⟹ s₂ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_RTC_SmallStep | [742, 1] | [753, 17] | intro hS | Ss : Stmt × State
t : State
⊢ RTC SmallStep Ss (Stmt.skip, t) → Ss ⟹ t | Ss : Stmt × State
t : State
hS : RTC SmallStep Ss (Stmt.skip, t)
⊢ Ss ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_RTC_SmallStep | [742, 1] | [753, 17] | induction hS using RTC.head_induction_on with
| refl =>
apply BigStep.skip
| head Ss Ss' hST hsmallT ih =>
cases Ss' with
| mk S' s' =>
apply BigStep_of_SmallStep_of_BigStep hST
apply ih | Ss : Stmt × State
t : State
hS : RTC SmallStep Ss (Stmt.skip, t)
⊢ Ss ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_RTC_SmallStep | [742, 1] | [753, 17] | apply BigStep.skip | case refl
Ss : Stmt × State
t : State
⊢ (Stmt.skip, t) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_RTC_SmallStep | [742, 1] | [753, 17] | cases Ss' with
| mk S' s' =>
apply BigStep_of_SmallStep_of_BigStep hST
apply ih | case head
Ss✝ : Stmt × State
t : State
Ss Ss' : Stmt × State
hST : Ss ⇒ Ss'
hsmallT : RTC SmallStep Ss' (Stmt.skip, t)
ih : Ss' ⟹ t
⊢ Ss ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_RTC_SmallStep | [742, 1] | [753, 17] | apply BigStep_of_SmallStep_of_BigStep hST | case head.mk
Ss✝ : Stmt × State
t : State
Ss : Stmt × State
S' : Stmt
s' : State
hST : Ss ⇒ (S', s')
hsmallT : RTC SmallStep (S', s') (Stmt.skip, t)
ih : (S', s') ⟹ t
⊢ Ss ⟹ t | case head.mk
Ss✝ : Stmt × State
t : State
Ss : Stmt × State
S' : Stmt
s' : State
hST : Ss ⇒ (S', s')
hsmallT : RTC SmallStep (S', s') (Stmt.skip, t)
ih : (S', s') ⟹ t
⊢ (S', s') ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe09_OperationalSemantics_Demo.lean | LoVe.BigStep_of_RTC_SmallStep | [742, 1] | [753, 17] | apply ih | case head.mk
Ss✝ : Stmt × State
t : State
Ss : Stmt × State
S' : Stmt
s' : State
hST : Ss ⇒ (S', s')
hsmallT : RTC SmallStep (S', s') (Stmt.skip, t)
ih : (S', s') ⟹ t
⊢ (S', s') ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bd | [45, 1] | [60, 18] | intro_and | a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b ∧ d | case left
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b
case right
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ d |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bd | [45, 1] | [60, 18] | repeat' sorry | case left
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b
case right
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ d | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bd | [45, 1] | [60, 18] | sorry | case right
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ d | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bacb | [62, 1] | [87, 18] | intro_and | a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b ∧ a ∧ c ∧ b | case left
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b
case right.left
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ a
case right.right.left
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ c
case right.right.right
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bacb | [62, 1] | [87, 18] | repeat' sorry | case left
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b
case right.left
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ a
case right.right.left
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ c
case right.right.right
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bacb | [62, 1] | [87, 18] | sorry | case right.right.right
a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bd_again | [129, 1] | [143, 10] | intro h | a b c d : Prop
⊢ a ∧ (b ∧ c) ∧ d → b ∧ d | a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b ∧ d |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bd_again | [129, 1] | [143, 10] | cases_and | a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b ∧ d | case intro.intro.intro
a b c d : Prop
left : a
right : d
left_1 : b
right_1 : c
⊢ b ∧ d |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bd_again | [129, 1] | [143, 10] | sorry | case intro.intro.intro
a b c d : Prop
left : a
right : d
left_1 : b
right_1 : c
⊢ b ∧ d | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bd_over_again | [155, 1] | [157, 16] | destro_and | a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b ∧ d | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcd_bacb_again | [159, 1] | [161, 16] | destro_and | a b c d : Prop
h : a ∧ (b ∧ c) ∧ d
⊢ b ∧ a ∧ c ∧ b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abd_bacb_again | [163, 1] | [175, 10] | destro_and | a b c d : Prop
h : a ∧ b ∧ d
⊢ b ∧ a ∧ c ∧ b | case intro.intro.right.right.left
a b c d : Prop
left : a
left_1 : b
right : d
⊢ c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abd_bacb_again | [163, 1] | [175, 10] | sorry | case intro.intro.right.right.left
a b c d : Prop
left : a
left_1 : b
right : d
⊢ c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.ab | [180, 1] | [182, 16] | destro_and | a b : Prop
h : a ∨ b
⊢ a ∨ b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcdef_1 | [184, 1] | [186, 16] | destro_and | a b c d e f : Prop
h : a ∧ b ∧ c ∧ d ∧ e ∧ f
⊢ f ∧ e ∧ f ∧ a ∧ d ∧ b ∧ c ∧ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcdef_2 | [188, 1] | [190, 16] | destro_and | a b c d e f : Prop
h : a ∧ (b ∧ (c ∧ d) ∧ e) ∧ f
⊢ f ∧ e ∧ f ∧ a ∧ d ∧ b ∧ c ∧ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.abcdef_3 | [192, 1] | [194, 16] | destro_and | a b c d e f : Prop
h : a ∧ b ∧ c ∧ d ∧ e ∧ f
⊢ f ∧ e ∧ f ∧ a ∧ d ∧ b ∧ c ∧ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab10Solution.lean | LoVe.List.a_property_of_reverse | [251, 1] | [256, 30] | apply List.reverse_concat | α : Type
xs : List α
a : α
⊢ List.reverse (List.concat xs a) = a :: List.reverse xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab9Solution.lean | LoVe.Fraction.ext | [23, 1] | [32, 36] | cases a with
| mk na da =>
cases b with
| mk nb db =>
simp at *
exact And.intro hnum hdenom | a b : Fraction
hnum : a.num = b.num
hdenom : a.denom = b.denom
⊢ a = b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab9Solution.lean | LoVe.Fraction.ext | [23, 1] | [32, 36] | cases b with
| mk nb db =>
simp at *
exact And.intro hnum hdenom | case mk
b : Fraction
na da : ℤ
denom_Neq_zero✝ : da ≠ 0
hnum : { num := na, denom := da, denom_Neq_zero := denom_Neq_zero✝ }.num = b.num
hdenom : { num := na, denom := da, denom_Neq_zero := denom_Neq_zero✝ }.denom = b.denom
⊢ { num := na, denom := da, denom_Neq_zero := denom_Neq_zero✝ } = b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab9Solution.lean | LoVe.Fraction.ext | [23, 1] | [32, 36] | simp at * | case mk.mk
na da : ℤ
denom_Neq_zero✝¹ : da ≠ 0
nb db : ℤ
denom_Neq_zero✝ : db ≠ 0
hnum :
{ num := na, denom := da, denom_Neq_zero := denom_Neq_zero✝¹ }.num =
{ num := nb, denom := db, denom_Neq_zero := denom_Neq_zero✝ }.num
hdenom :
{ num := na, denom := da, denom_Neq_zero := denom_Neq_zero✝¹ }.denom =
{ num := nb, denom := db, denom_Neq_zero := denom_Neq_zero✝ }.denom
⊢ { num := na, denom := da, denom_Neq_zero := denom_Neq_zero✝¹ } =
{ num := nb, denom := db, denom_Neq_zero := denom_Neq_zero✝ } | case mk.mk
na da : ℤ
denom_Neq_zero✝¹ : da ≠ 0
nb db : ℤ
denom_Neq_zero✝ : db ≠ 0
hnum : na = nb
hdenom : da = db
⊢ na = nb ∧ da = db |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab9Solution.lean | LoVe.Fraction.ext | [23, 1] | [32, 36] | exact And.intro hnum hdenom | case mk.mk
na da : ℤ
denom_Neq_zero✝¹ : da ≠ 0
nb db : ℤ
denom_Neq_zero✝ : db ≠ 0
hnum : na = nb
hdenom : da = db
⊢ na = nb ∧ da = db | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6.lean | LoVe.BigStepEquiv.refl | [131, 1] | [135, 11] | rfl | S : Stmt
s t : State
⊢ (S, s) ⟹ t ↔ (S, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework2.lean | LoVe.BackwardProofs.square_square | [199, 1] | [201, 60] | intro h | a b c : ℕ
⊢ (a ^ 2) ^ 2 + (b ^ 2) ^ 2 = (c ^ 2) ^ 2 → a ^ 4 + b ^ 4 = c ^ 4 | a b c : ℕ
h : (a ^ 2) ^ 2 + (b ^ 2) ^ 2 = (c ^ 2) ^ 2
⊢ a ^ 4 + b ^ 4 = c ^ 4 |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework2.lean | LoVe.BackwardProofs.square_square | [199, 1] | [201, 60] | rw [←pow_mul, ←pow_mul, ←pow_mul] at h | a b c : ℕ
h : (a ^ 2) ^ 2 + (b ^ 2) ^ 2 = (c ^ 2) ^ 2
⊢ a ^ 4 + b ^ 4 = c ^ 4 | a b c : ℕ
h : a ^ (2 * 2) + b ^ (2 * 2) = c ^ (2 * 2)
⊢ a ^ 4 + b ^ 4 = c ^ 4 |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework2.lean | LoVe.BackwardProofs.square_square | [199, 1] | [201, 60] | exact h | a b c : ℕ
h : a ^ (2 * 2) + b ^ (2 * 2) = c ^ (2 * 2)
⊢ a ^ 4 + b ^ 4 = c ^ 4 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.ring_example | [218, 1] | [220, 10] | ring | a b : Int2
⊢ (a + b) ^ 3 = a ^ 3 + 3 * a ^ 2 * b + 3 * a * b ^ 2 + b ^ 3 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.neg_mul_neg_Nat | [243, 1] | [245, 10] | simp | n : ℕ
z : ℤ
⊢ -z * -↑n = z * ↑n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.neg_Nat_mul_neg | [254, 1] | [256, 10] | simp | n : ℕ
z : ℤ
⊢ -↑n * -z = ↑n * z | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.Eq_coe_int_imp_Eq_Nat | [263, 1] | [266, 20] | norm_cast at h | m n : ℕ
h : ↑m = ↑n
⊢ m = n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.Nat_coe_Int_add_eq_add_Nat_coe_Int | [269, 1] | [271, 15] | norm_cast | m n : ℕ
⊢ ↑m + ↑n = ↑(m + n) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.List_duplicates_example | [292, 1] | [294, 12] | decide | ⊢ [2, 3, 3, 4] ≠ [2, 3, 4] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.List_order_example | [296, 1] | [298, 12] | decide | ⊢ [4, 3, 2] ≠ [2, 3, 4] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.Multiset_duplicates_example | [300, 1] | [302, 12] | decide | ⊢ {2, 3, 3, 4} ≠ {2, 3, 4} | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.Multiset_order_example | [304, 1] | [306, 12] | decide | ⊢ {2, 3, 4} = {4, 3, 2} | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.Finset_duplicates_example | [308, 1] | [310, 12] | decide | ⊢ {2, 3, 3, 4} = {2, 3, 4} | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.Finset_order_example | [312, 1] | [314, 12] | decide | ⊢ {2, 3, 4} = {4, 3, 2} | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe13_BasicMathematicalStructures_Demo.lean | LoVe.list.length.Preorder_example | [405, 1] | [407, 12] | decide | ⊢ [1] > [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square | [133, 1] | [147, 51] | simp only [add_mul, mul_add] | a b : ℕ
⊢ (a + b) * (a + b) = a * (a + b) + b * (a + b) | a b : ℕ
⊢ a * a + b * a + (a * b + b * b) = a * a + a * b + (b * a + b * b) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square | [133, 1] | [147, 51] | ac_rfl | a b : ℕ
⊢ a * a + b * a + (a * b + b * b) = a * a + a * b + (b * a + b * b) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square | [133, 1] | [147, 51] | simp only [add_mul, mul_add] | a b : ℕ
⊢ a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b | a b : ℕ
⊢ a * a + a * b + (b * a + b * b) = a * a + a * b + b * a + b * b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square | [133, 1] | [147, 51] | ac_rfl | a b : ℕ
⊢ a * a + a * b + (b * a + b * b) = a * a + a * b + b * a + b * b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square | [133, 1] | [147, 51] | simp only [mul_comm] | a b : ℕ
⊢ a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square | [133, 1] | [147, 51] | simp only [Nat.two_mul, add_mul, add_assoc] | a b : ℕ
⊢ a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | simp only [add_mul, mul_add] | a b : ℕ
⊢ (a + b) * (a + b) = a * (a + b) + b * (a + b) | a b : ℕ
⊢ a * a + b * a + (a * b + b * b) = a * a + a * b + (b * a + b * b) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | ac_rfl | a b : ℕ
⊢ a * a + b * a + (a * b + b * b) = a * a + a * b + (b * a + b * b) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | simp only [add_mul, mul_add] | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
⊢ a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
⊢ a * a + a * b + (b * a + b * b) = a * a + a * b + b * a + b * b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | ac_rfl | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
⊢ a * a + a * b + (b * a + b * b) = a * a + a * b + b * a + b * b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | simp only [mul_comm] | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
⊢ a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | simp only [Nat.two_mul, add_mul, add_assoc] | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
h3 : a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b
⊢ a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | rw [h1] | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
h3 : a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b
h4 : a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b
⊢ (a + b) * (a + b) = a * a + 2 * a * b + b * b | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
h3 : a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b
h4 : a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b
⊢ a * (a + b) + b * (a + b) = a * a + 2 * a * b + b * b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | rw [h2] | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
h3 : a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b
h4 : a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b
⊢ a * (a + b) + b * (a + b) = a * a + 2 * a * b + b * b | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
h3 : a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b
h4 : a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b
⊢ a * a + a * b + b * a + b * b = a * a + 2 * a * b + b * b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | rw [h3] | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
h3 : a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b
h4 : a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b
⊢ a * a + a * b + b * a + b * b = a * a + 2 * a * b + b * b | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
h3 : a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b
h4 : a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b
⊢ a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.binomial_square₂ | [156, 1] | [175, 14] | rw [h4] | a b : ℕ
h1 : (a + b) * (a + b) = a * (a + b) + b * (a + b)
h2 : a * (a + b) + b * (a + b) = a * a + a * b + b * a + b * b
h3 : a * a + a * b + b * a + b * b = a * a + a * b + a * b + b * b
h4 : a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b
⊢ a * a + a * b + a * b + b * b = a * a + 2 * a * b + b * b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.All.proof_of_False | [188, 1] | [196, 23] | have hwrong : (∀x, x = 0 ∧ True) ↔ True :=
All.one_point_wrong 0 (fun _ ↦ True) | ⊢ False | hwrong : (∀ (x : ℕ), x = 0 ∧ True) ↔ True
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.All.proof_of_False | [188, 1] | [196, 23] | simp at hwrong | hwrong : (∀ (x : ℕ), x = 0 ∧ True) ↔ True
⊢ False | hwrong : ∀ (x : ℕ), x = 0
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.All.proof_of_False | [188, 1] | [196, 23] | have hone_eq_zero : 1 = 0 :=
hwrong 1 | hwrong : ∀ (x : ℕ), x = 0
⊢ False | hwrong : ∀ (x : ℕ), x = 0
hone_eq_zero : 1 = 0
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.All.proof_of_False | [188, 1] | [196, 23] | cases hone_eq_zero | hwrong : ∀ (x : ℕ), x = 0
hone_eq_zero : 1 = 0
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.Exists.proof_of_False | [206, 1] | [214, 23] | have hwrong : (∃x, x ≠ 0) ↔ False :=
Exists.one_point_wrong 0 (fun _ ↦ False) | ⊢ False | hwrong : (∃ x, x ≠ 0) ↔ False
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.Exists.proof_of_False | [206, 1] | [214, 23] | simp at hwrong | hwrong : (∃ x, x ≠ 0) ↔ False
⊢ False | hwrong : ∀ (x : ℕ), x = 0
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.Exists.proof_of_False | [206, 1] | [214, 23] | have hone_eq_zero : 1 = 0 :=
hwrong 1 | hwrong : ∀ (x : ℕ), x = 0
⊢ False | hwrong : ∀ (x : ℕ), x = 0
hone_eq_zero : 1 = 0
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab3Solution.lean | LoVe.Exists.proof_of_False | [206, 1] | [214, 23] | cases hone_eq_zero | hwrong : ∀ (x : ℕ), x = 0
hone_eq_zero : 1 = 0
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.Odd_1 | [30, 9] | [34, 14] | intro ho1 | ⊢ Odd 1 | ho1 : Even 1
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.Odd_1 | [30, 9] | [34, 14] | cases ho1 | ho1 : Even 1
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.Odd_3 | [38, 1] | [44, 16] | intro ho3 | ⊢ Odd 3 | ho3 : Even 3
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.Odd_3 | [38, 1] | [44, 16] | cases ho3 with
| add_two _ ho1 =>
cases ho1 | ho3 : Even 3
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.Odd_3 | [38, 1] | [44, 16] | cases ho1 | case add_two
ho1 : Even 1
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.odd_5 | [46, 1] | [54, 18] | intro ho5 | ⊢ Odd 5 | ho5 : Even 5
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.odd_5 | [46, 1] | [54, 18] | cases ho5 with
| add_two _ ho3 =>
cases ho3 with
| add_two _ ho1 =>
cases ho1 | ho5 : Even 5
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.odd_5 | [46, 1] | [54, 18] | cases ho3 with
| add_two _ ho1 =>
cases ho1 | case add_two
ho3 : Even 3
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.odd_5 | [46, 1] | [54, 18] | cases ho1 | case add_two.add_two
ho1 : Even 1
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.Even_two_times | [58, 1] | [65, 27] | apply Even.add_two | m : ℕ
⊢ Even (2 * (m + 1)) | case a
m : ℕ
⊢ Even (Nat.mul 2 (Nat.add m 0)) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.Even_two_times | [58, 1] | [65, 27] | simp | case a
m : ℕ
⊢ Even (Nat.mul 2 (Nat.add m 0)) | case a
m : ℕ
⊢ Even (2 * m) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.Even_two_times | [58, 1] | [65, 27] | apply Even_two_times | case a
m : ℕ
⊢ Even (2 * m) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.not_ServAhead_advRecv | [92, 1] | [96, 12] | intro h | ⊢ ¬ServAhead Score.advRecv | h : ServAhead Score.advRecv
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.not_ServAhead_advRecv | [92, 1] | [96, 12] | cases h | h : ServAhead Score.advRecv
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.not_ServAhead_gameRecv | [102, 1] | [106, 12] | intro h | ⊢ ¬ServAhead Score.gameRecv | h : ServAhead Score.gameRecv
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.not_ServAhead_gameRecv | [102, 1] | [106, 12] | cases h | h : ServAhead Score.gameRecv
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.mirror_IsFull | [124, 1] | [131, 15] | intro t fmt | α : Type
⊢ ∀ (t : BTree α), IsFull (mirror t) → IsFull t | α : Type
t : BTree α
fmt : IsFull (mirror t)
⊢ IsFull t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab5Solution.lean | LoVe.mirror_IsFull | [124, 1] | [131, 15] | have fmmt : IsFull (mirror (mirror t)) :=
IsFull_mirror _ fmt | α : Type
t : BTree α
fmt : IsFull (mirror t)
⊢ IsFull t | α : Type
t : BTree α
fmt : IsFull (mirror t)
fmmt : IsFull (mirror (mirror t))
⊢ IsFull t |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.