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stringclasses 147
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stringlengths 7
101
| full_name
stringlengths 1
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| start
stringlengths 6
10
| end
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stringlengths 1
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https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_and_iff_or_not | [10, 1] | [28, 4] | exact h | case neg.h
p q r : Prop
hnand : ¬(p ∧ q)
h : ¬p
⊢ ¬p | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_and_iff_or_not | [10, 1] | [28, 4] | intros hnor hand | case mpr
p q r : Prop
⊢ ¬p ∨ ¬q → ¬(p ∧ q) | case mpr
p q r : Prop
hnor : ¬p ∨ ¬q
hand : p ∧ q
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_and_iff_or_not | [10, 1] | [28, 4] | rcases hand with ⟨hp, hq⟩ | case mpr
p q r : Prop
hnor : ¬p ∨ ¬q
hand : p ∧ q
⊢ False | case mpr.intro
p q r : Prop
hnor : ¬p ∨ ¬q
hp : p
hq : q
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_and_iff_or_not | [10, 1] | [28, 4] | cases hnor with
| inl hnp => exact hnp hp
| inr hnq => exact hnq hq | case mpr.intro
p q r : Prop
hnor : ¬p ∨ ¬q
hp : p
hq : q
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_and_iff_or_not | [10, 1] | [28, 4] | exact hnp hp | case mpr.intro.inl
p q r : Prop
hp : p
hq : q
hnp : ¬p
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_and_iff_or_not | [10, 1] | [28, 4] | exact hnq hq | case mpr.intro.inr
p q r : Prop
hp : p
hq : q
hnq : ¬q
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | constructor | p q r : Prop
⊢ ¬(p ∨ q) ↔ ¬p ∧ ¬q | case mp
p q r : Prop
⊢ ¬(p ∨ q) → ¬p ∧ ¬q
case mpr
p q r : Prop
⊢ ¬p ∧ ¬q → ¬(p ∨ q) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | { intro hnor
constructor
{ intro hp
exact hnor (Or.inl hp)
}
{ intro hq
exact hnor (Or.inr hq)
}
} | case mp
p q r : Prop
⊢ ¬(p ∨ q) → ¬p ∧ ¬q
case mpr
p q r : Prop
⊢ ¬p ∧ ¬q → ¬(p ∨ q) | case mpr
p q r : Prop
⊢ ¬p ∧ ¬q → ¬(p ∨ q) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | {
intros hnand hor
rcases hnand with ⟨hnp, hnq⟩
cases hor with
| inl hp => exact hnp hp
| inr hq => exact hnq hq
} | case mpr
p q r : Prop
⊢ ¬p ∧ ¬q → ¬(p ∨ q) | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | intro hnor | case mp
p q r : Prop
⊢ ¬(p ∨ q) → ¬p ∧ ¬q | case mp
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬p ∧ ¬q |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | constructor | case mp
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬p ∧ ¬q | case mp.left
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬p
case mp.right
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬q |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | { intro hp
exact hnor (Or.inl hp)
} | case mp.left
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬p
case mp.right
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬q | case mp.right
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬q |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | { intro hq
exact hnor (Or.inr hq)
} | case mp.right
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬q | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | intro hp | case mp.left
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬p | case mp.left
p q r : Prop
hnor : ¬(p ∨ q)
hp : p
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | exact hnor (Or.inl hp) | case mp.left
p q r : Prop
hnor : ¬(p ∨ q)
hp : p
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | intro hq | case mp.right
p q r : Prop
hnor : ¬(p ∨ q)
⊢ ¬q | case mp.right
p q r : Prop
hnor : ¬(p ∨ q)
hq : q
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | exact hnor (Or.inr hq) | case mp.right
p q r : Prop
hnor : ¬(p ∨ q)
hq : q
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | intros hnand hor | case mpr
p q r : Prop
⊢ ¬p ∧ ¬q → ¬(p ∨ q) | case mpr
p q r : Prop
hnand : ¬p ∧ ¬q
hor : p ∨ q
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | rcases hnand with ⟨hnp, hnq⟩ | case mpr
p q r : Prop
hnand : ¬p ∧ ¬q
hor : p ∨ q
⊢ False | case mpr.intro
p q r : Prop
hor : p ∨ q
hnp : ¬p
hnq : ¬q
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | cases hor with
| inl hp => exact hnp hp
| inr hq => exact hnq hq | case mpr.intro
p q r : Prop
hor : p ∨ q
hnp : ¬p
hnq : ¬q
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | exact hnp hp | case mpr.intro.inl
p q r : Prop
hnp : ¬p
hnq : ¬q
hp : p
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/Foundations.lean | not_or_iff_and_not | [30, 1] | [50, 4] | exact hnq hq | case mpr.intro.inr
p q r : Prop
hnp : ¬p
hnq : ¬q
hq : q
⊢ False | no goals |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewriteOrd.lean | MotivatedTree.funext_ord | [204, 1] | [204, 113] | exact h | α : Type u
β : Type v
inst✝ : Preorder β
f g : α → β
h : ∀ (a : α), f a ≤ g a
⊢ f ≤ g | no goals |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Demo.lean | Cantor | [4, 1] | [12, 33] | motivated_proof
tree_rewrite_def [1, 1, 1, 2]
tree_push_neg [1, 1]
lib_rewrite [1, 1, 1, 2, 0, 1] Set.ext_iff [1, 1, 1, 1, 1, 2]
tree_push_neg [1, 1, 1, 1]
lib_rewrite [1, 1, 2, 0, 1] not_iff [1, 1, 1, 1, 1]
unify_forall_exists [1, 1, 1]
lib_apply refl [1, 1, 1, 1, 2] | ⊢ ∀ (X : Type u) (f : X → Set X), ¬Function.Surjective f | no goals |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Demo.lean | Cantor | [4, 1] | [12, 33] | tree_rewrite_def [1, 1, 1, 2] | ⊢ ∀ X : Type u, f : X → Set X⠀
¬Function.Surjective f | ⊢ ∀ X : Type u, f : X → Set X⠀
¬∀ b⋆ : Set X, ∃ a : X⠀
f a = b⋆ |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Demo.lean | Cantor | [4, 1] | [12, 33] | tree_push_neg [1, 1] | ⊢ ∀ X : Type u, f : X → Set X⠀
¬∀ b⋆ : Set X, ∃ a : X⠀
f a = b⋆ | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ x_1 : X⠀
¬f x_1 = x• |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Demo.lean | Cantor | [4, 1] | [12, 33] | lib_rewrite [1, 1, 1, 2, 0, 1] Set.ext_iff [1, 1, 1, 1, 1, 2] | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ x_1 : X⠀
¬f x_1 = x• | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ x_1 : X⠀
¬(∀ x_2⋆ : X⠀
x_2⋆ ∈ f x_1 ↔ x_2⋆ ∈ x•) |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Demo.lean | Cantor | [4, 1] | [12, 33] | tree_push_neg [1, 1, 1, 1] | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ x_1 : X⠀
¬(∀ x_2⋆ : X⠀
x_2⋆ ∈ f x_1 ↔ x_2⋆ ∈ x•) | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ x_1 : X, ∃ x_2• : X⠀
¬(x_2• ∈ f x_1 ↔ x_2• ∈ x•) |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Demo.lean | Cantor | [4, 1] | [12, 33] | lib_rewrite [1, 1, 2, 0, 1] not_iff [1, 1, 1, 1, 1] | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ x_1 : X, ∃ x_2• : X⠀
¬(x_2• ∈ f x_1 ↔ x_2• ∈ x•) | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ x_1 : X, ∃ x_2• : X⠀
¬x_2• ∈ f x_1 ↔ x_2• ∈ x• |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Demo.lean | Cantor | [4, 1] | [12, 33] | unify_forall_exists [1, 1, 1] | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ x_1 : X, ∃ x_2• : X⠀
¬x_2• ∈ f x_1 ↔ x_2• ∈ x• | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ a : X⠀
¬a ∈ f a ↔ a ∈ x• |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Demo.lean | Cantor | [4, 1] | [12, 33] | lib_apply refl [1, 1, 1, 1, 2] | ⊢ ∀ X : Type u, f : X → Set X, ∃ x• : Set X, ∀ a : X⠀
¬a ∈ f a ↔ a ∈ x• | no goals |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewrite.lean | MotivatedTree.imp_exists_iff | [157, 1] | [166, 19] | apply Iff.intro | α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
⊢ Imp p (_root_.Exists q) ↔ ∃ a, p → q a | case mp
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
⊢ Imp p (_root_.Exists q) → ∃ a, p → q a
case mpr
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
⊢ (∃ a, p → q a) → Imp p (_root_.Exists q) |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewrite.lean | MotivatedTree.imp_exists_iff | [157, 1] | [166, 19] | by_cases p | case mp
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
⊢ Imp p (_root_.Exists q) → ∃ a, p → q a
case mpr
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
⊢ (∃ a, p → q a) → Imp p (_root_.Exists q) | case pos
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : p
⊢ Imp p (_root_.Exists q) → ∃ a, p → q a
case neg
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : ¬p
⊢ Imp p (_root_.Exists q) → ∃ a, p → q a
case mpr
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
⊢ (∃ a, p → q a) → Imp p (_root_.Exists q) |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewrite.lean | MotivatedTree.imp_exists_iff | [157, 1] | [166, 19] | intro g | case pos
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : p
⊢ Imp p (_root_.Exists q) → ∃ a, p → q a | case pos
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : p
g : Imp p (_root_.Exists q)
⊢ ∃ a, p → q a |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewrite.lean | MotivatedTree.imp_exists_iff | [157, 1] | [166, 19] | have ⟨a, g⟩ := g ‹p› | case pos
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : p
g : Imp p (_root_.Exists q)
⊢ ∃ a, p → q a | case pos
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : p
g✝ : Imp p (_root_.Exists q)
a : α
g : q a
⊢ ∃ a, p → q a |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewrite.lean | MotivatedTree.imp_exists_iff | [157, 1] | [166, 19] | exact ⟨a, fun _ => g⟩ | case pos
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : p
g✝ : Imp p (_root_.Exists q)
a : α
g : q a
⊢ ∃ a, p → q a | no goals |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewrite.lean | MotivatedTree.imp_exists_iff | [157, 1] | [166, 19] | intro _ | case neg
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : ¬p
⊢ Imp p (_root_.Exists q) → ∃ a, p → q a | case neg
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
h✝ : ¬p
a✝ : Imp p (_root_.Exists q)
⊢ ∃ a, p → q a |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewrite.lean | MotivatedTree.imp_exists_iff | [157, 1] | [166, 19] | intro ⟨a, h⟩ g | case mpr
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
⊢ (∃ a, p → q a) → Imp p (_root_.Exists q) | case mpr
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
a : α
h : p → q a
g : p
⊢ _root_.Exists q |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | MotivatedMoves/Moves/TreeRewrite.lean | MotivatedTree.imp_exists_iff | [157, 1] | [166, 19] | exact ⟨a, h g⟩ | case mpr
α : Sort u_1
inst : Nonempty α
p : Prop
q : α → Prop
a : α
h : p → q a
g : p
⊢ _root_.Exists q | no goals |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Moves/TreeApply.lean | cantor_end | [13, 1] | [16, 43] | make_tree | ⊢ ∀ (X : Type u) (f : X → Set X), ∃ a, ∀ (a_1 : X), a_1 ∉ f a_1 ↔ a_1 ∈ a | ⊢ MotivatedTree.Forall (Type u) fun X =>
MotivatedTree.Forall (X → Set X) fun f =>
MotivatedTree.Exists (Set X) fun a => MotivatedTree.Forall X fun a_1 => MotivatedTree.Not (a_1 ∈ f a_1) ↔ a_1 ∈ a |
https://github.com/Human-Oriented-ATP/lean-tactics.git | a62b1d3dd89deaf243ff9536cb31a318ea91c628 | Tests/Moves/TreeApply.lean | cantor_end | [13, 1] | [16, 43] | lib_apply [1,1,1,1] refl [1, 1, 1, 1, 2] | ⊢ MotivatedTree.Forall (Type u) fun X =>
MotivatedTree.Forall (X → Set X) fun f =>
MotivatedTree.Exists (Set X) fun a => MotivatedTree.Forall X fun a_1 => MotivatedTree.Not (a_1 ∈ f a_1) ↔ a_1 ∈ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.two_mul | [46, 1] | [48, 10] | ring | n : ℕ
⊢ 2 * n = n + n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.add_sub_again | [50, 9] | [55, 61] | induction m with
| zero => simp
| succ m' ih => rw [Nat.succ_add, Nat.succ_sub_succ, ih] | m n : ℕ
⊢ m + n - m = n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.add_sub_again | [50, 9] | [55, 61] | simp | case zero
n : ℕ
⊢ Nat.zero + n - Nat.zero = n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.add_sub_again | [50, 9] | [55, 61] | rw [Nat.succ_add, Nat.succ_sub_succ, ih] | case succ
n m' : ℕ
ih : m' + n - m' = n
⊢ Nat.succ m' + n - Nat.succ m' = n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.sub_one_add | [57, 9] | [64, 12] | induction n with
| zero => aesop
| succ =>
rw [Nat.succ_add]
aesop | n m : ℕ
h : ¬n = 0
⊢ n - 1 + m = n + m - 1 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.sub_one_add | [57, 9] | [64, 12] | aesop | case zero
m : ℕ
h : ¬Nat.zero = 0
⊢ Nat.zero - 1 + m = Nat.zero + m - 1 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.sub_one_add | [57, 9] | [64, 12] | rw [Nat.succ_add] | case succ
m n_1 : ℕ
n_ih : ¬n_1 = 0 → n_1 - 1 + m = n_1 + m - 1
h : ¬Nat.succ n_1 = 0
⊢ Nat.succ n_1 - 1 + m = Nat.succ n_1 + m - 1 | case succ
m n_1 : ℕ
n_ih : ¬n_1 = 0 → n_1 - 1 + m = n_1 + m - 1
h : ¬Nat.succ n_1 = 0
⊢ Nat.succ n_1 - 1 + m = Nat.succ (n_1 + m) - 1 |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.sub_one_add | [57, 9] | [64, 12] | aesop | case succ
m n_1 : ℕ
n_ih : ¬n_1 = 0 → n_1 - 1 + m = n_1 + m - 1
h : ¬Nat.succ n_1 = 0
⊢ Nat.succ n_1 - 1 + m = Nat.succ (n_1 + m) - 1 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_lt_plus_right | [66, 9] | [73, 37] | apply Iff.intro | l m n : ℕ
⊢ m + l < n + l ↔ m < n | case mp
l m n : ℕ
⊢ m + l < n + l → m < n
case mpr
l m n : ℕ
⊢ m < n → m + l < n + l |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_lt_plus_right | [66, 9] | [73, 37] | { intro h
apply Nat.lt_of_add_lt_add_right h } | case mp
l m n : ℕ
⊢ m + l < n + l → m < n
case mpr
l m n : ℕ
⊢ m < n → m + l < n + l | case mpr
l m n : ℕ
⊢ m < n → m + l < n + l |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_lt_plus_right | [66, 9] | [73, 37] | { intro h
apply Nat.add_lt_add_right h } | case mpr
l m n : ℕ
⊢ m < n → m + l < n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_lt_plus_right | [66, 9] | [73, 37] | intro h | case mp
l m n : ℕ
⊢ m + l < n + l → m < n | case mp
l m n : ℕ
h : m + l < n + l
⊢ m < n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_lt_plus_right | [66, 9] | [73, 37] | apply Nat.lt_of_add_lt_add_right h | case mp
l m n : ℕ
h : m + l < n + l
⊢ m < n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_lt_plus_right | [66, 9] | [73, 37] | intro h | case mpr
l m n : ℕ
⊢ m < n → m + l < n + l | case mpr
l m n : ℕ
h : m < n
⊢ m + l < n + l |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_lt_plus_right | [66, 9] | [73, 37] | apply Nat.add_lt_add_right h | case mpr
l m n : ℕ
h : m < n
⊢ m + l < n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_le_plus_right | [75, 9] | [82, 37] | apply Iff.intro | l m n : ℕ
⊢ m + l ≤ n + l ↔ m ≤ n | case mp
l m n : ℕ
⊢ m + l ≤ n + l → m ≤ n
case mpr
l m n : ℕ
⊢ m ≤ n → m + l ≤ n + l |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_le_plus_right | [75, 9] | [82, 37] | { intro h
apply Nat.le_of_add_le_add_right h } | case mp
l m n : ℕ
⊢ m + l ≤ n + l → m ≤ n
case mpr
l m n : ℕ
⊢ m ≤ n → m + l ≤ n + l | case mpr
l m n : ℕ
⊢ m ≤ n → m + l ≤ n + l |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_le_plus_right | [75, 9] | [82, 37] | { intro h
apply Nat.add_le_add_right h } | case mpr
l m n : ℕ
⊢ m ≤ n → m + l ≤ n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_le_plus_right | [75, 9] | [82, 37] | intro h | case mp
l m n : ℕ
⊢ m + l ≤ n + l → m ≤ n | case mp
l m n : ℕ
h : m + l ≤ n + l
⊢ m ≤ n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_le_plus_right | [75, 9] | [82, 37] | apply Nat.le_of_add_le_add_right h | case mp
l m n : ℕ
h : m + l ≤ n + l
⊢ m ≤ n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_le_plus_right | [75, 9] | [82, 37] | intro h | case mpr
l m n : ℕ
⊢ m ≤ n → m + l ≤ n + l | case mpr
l m n : ℕ
h : m ≤ n
⊢ m + l ≤ n + l |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.plus_le_plus_right | [75, 9] | [82, 37] | apply Nat.add_le_add_right h | case mpr
l m n : ℕ
h : m ≤ n
⊢ m + l ≤ n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | apply Iff.intro | m n : ℕ
p : Prop
hge : m ≥ n
⊢ m < n → p ↔ True | case mp
m n : ℕ
p : Prop
hge : m ≥ n
⊢ (m < n → p) → True
case mpr
m n : ℕ
p : Prop
hge : m ≥ n
⊢ True → m < n → p |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | { intro himp
apply True.intro } | case mp
m n : ℕ
p : Prop
hge : m ≥ n
⊢ (m < n → p) → True
case mpr
m n : ℕ
p : Prop
hge : m ≥ n
⊢ True → m < n → p | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
⊢ True → m < n → p |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | { intro htrue
intro hlt
have hle : n ≤ m :=
hge
rw [←Nat.not_lt_eq] at hle
apply False.elim
exact hle hlt } | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
⊢ True → m < n → p | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | intro himp | case mp
m n : ℕ
p : Prop
hge : m ≥ n
⊢ (m < n → p) → True | case mp
m n : ℕ
p : Prop
hge : m ≥ n
himp : m < n → p
⊢ True |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | apply True.intro | case mp
m n : ℕ
p : Prop
hge : m ≥ n
himp : m < n → p
⊢ True | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | intro htrue | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
⊢ True → m < n → p | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
⊢ m < n → p |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | intro hlt | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
⊢ m < n → p | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
hlt : m < n
⊢ p |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | have hle : n ≤ m :=
hge | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
hlt : m < n
⊢ p | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
hlt : m < n
hle : n ≤ m
⊢ p |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | rw [←Nat.not_lt_eq] at hle | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
hlt : m < n
hle : n ≤ m
⊢ p | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
hlt : m < n
hle : ¬m < n
⊢ p |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | apply False.elim | case mpr
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
hlt : m < n
hle : ¬m < n
⊢ p | case mpr.h
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
hlt : m < n
hle : ¬m < n
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_lt_imp | [84, 9] | [96, 22] | exact hle hlt | case mpr.h
m n : ℕ
p : Prop
hge : m ≥ n
htrue : True
hlt : m < n
hle : ¬m < n
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.lt_succ | [98, 9] | [103, 31] | apply Iff.intro | m n : ℕ
⊢ Nat.succ m < Nat.succ n ↔ m < n | case mp
m n : ℕ
⊢ Nat.succ m < Nat.succ n → m < n
case mpr
m n : ℕ
⊢ m < n → Nat.succ m < Nat.succ n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.lt_succ | [98, 9] | [103, 31] | { apply Nat.lt_of_succ_lt_succ } | case mp
m n : ℕ
⊢ Nat.succ m < Nat.succ n → m < n
case mpr
m n : ℕ
⊢ m < n → Nat.succ m < Nat.succ n | case mpr
m n : ℕ
⊢ m < n → Nat.succ m < Nat.succ n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.lt_succ | [98, 9] | [103, 31] | { apply Nat.succ_lt_succ } | case mpr
m n : ℕ
⊢ m < n → Nat.succ m < Nat.succ n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.lt_succ | [98, 9] | [103, 31] | apply Nat.lt_of_succ_lt_succ | case mp
m n : ℕ
⊢ Nat.succ m < Nat.succ n → m < n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.lt_succ | [98, 9] | [103, 31] | apply Nat.succ_lt_succ | case mpr
m n : ℕ
⊢ m < n → Nat.succ m < Nat.succ n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_succ | [105, 9] | [110, 31] | apply Iff.intro | m n : ℕ
⊢ Nat.succ m ≤ Nat.succ n ↔ m ≤ n | case mp
m n : ℕ
⊢ Nat.succ m ≤ Nat.succ n → m ≤ n
case mpr
m n : ℕ
⊢ m ≤ n → Nat.succ m ≤ Nat.succ n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_succ | [105, 9] | [110, 31] | { apply Nat.le_of_succ_le_succ } | case mp
m n : ℕ
⊢ Nat.succ m ≤ Nat.succ n → m ≤ n
case mpr
m n : ℕ
⊢ m ≤ n → Nat.succ m ≤ Nat.succ n | case mpr
m n : ℕ
⊢ m ≤ n → Nat.succ m ≤ Nat.succ n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_succ | [105, 9] | [110, 31] | { apply Nat.succ_le_succ } | case mpr
m n : ℕ
⊢ m ≤ n → Nat.succ m ≤ Nat.succ n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_succ | [105, 9] | [110, 31] | apply Nat.le_of_succ_le_succ | case mp
m n : ℕ
⊢ Nat.succ m ≤ Nat.succ n → m ≤ n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Nat.le_succ | [105, 9] | [110, 31] | apply Nat.succ_le_succ | case mpr
m n : ℕ
⊢ m ≤ n → Nat.succ m ≤ Nat.succ n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | apply funext | ⊢ Int.neg ∘ Int.neg = id | case h
⊢ ∀ (x : ℤ), (Int.neg ∘ Int.neg) x = id x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | intro i | case h
⊢ ∀ (x : ℤ), (Int.neg ∘ Int.neg) x = id x | case h
i : ℤ
⊢ (Int.neg ∘ Int.neg) i = id i |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | simp | case h
i : ℤ
⊢ (Int.neg ∘ Int.neg) i = id i | case h
i : ℤ
⊢ Int.neg (Int.neg i) = i |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | cases i with
| ofNat n =>
{ simp [Int.neg]
cases n
{ simp }
{ simp [Int.negOfNat] } }
| negSucc n =>
{ simp [Int.neg]
have hnp1 : (↑n + 1 : ℤ) = ↑(n + 1) :=
by simp
rw [hnp1]
rfl } | case h
i : ℤ
⊢ Int.neg (Int.neg i) = i | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | simp [Int.neg] | case h.ofNat
n : ℕ
⊢ Int.neg (Int.neg (Int.ofNat n)) = Int.ofNat n | case h.ofNat
n : ℕ
⊢ (match Int.negOfNat n with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | cases n | case h.ofNat
n : ℕ
⊢ (match Int.negOfNat n with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑n | case h.ofNat.zero
⊢ (match Int.negOfNat Nat.zero with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑Nat.zero
case h.ofNat.succ
n_1 : ℕ
⊢ (match Int.negOfNat (Nat.succ n_1) with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑(Nat.succ n_1) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | { simp } | case h.ofNat.zero
⊢ (match Int.negOfNat Nat.zero with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑Nat.zero
case h.ofNat.succ
n_1 : ℕ
⊢ (match Int.negOfNat (Nat.succ n_1) with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑(Nat.succ n_1) | case h.ofNat.succ
n_1 : ℕ
⊢ (match Int.negOfNat (Nat.succ n_1) with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑(Nat.succ n_1) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | { simp [Int.negOfNat] } | case h.ofNat.succ
n_1 : ℕ
⊢ (match Int.negOfNat (Nat.succ n_1) with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑(Nat.succ n_1) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | simp | case h.ofNat.zero
⊢ (match Int.negOfNat Nat.zero with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑Nat.zero | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | simp [Int.negOfNat] | case h.ofNat.succ
n_1 : ℕ
⊢ (match Int.negOfNat (Nat.succ n_1) with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
↑(Nat.succ n_1) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | simp [Int.neg] | case h.negSucc
n : ℕ
⊢ Int.neg (Int.neg (Int.negSucc n)) = Int.negSucc n | case h.negSucc
n : ℕ
⊢ (match ↑n + 1 with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
Int.negSucc n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | have hnp1 : (↑n + 1 : ℤ) = ↑(n + 1) :=
by simp | case h.negSucc
n : ℕ
⊢ (match ↑n + 1 with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
Int.negSucc n | case h.negSucc
n : ℕ
hnp1 : ↑n + 1 = ↑(n + 1)
⊢ (match ↑n + 1 with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
Int.negSucc n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | rw [hnp1] | case h.negSucc
n : ℕ
hnp1 : ↑n + 1 = ↑(n + 1)
⊢ (match ↑n + 1 with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
Int.negSucc n | case h.negSucc
n : ℕ
hnp1 : ↑n + 1 = ↑(n + 1)
⊢ (match ↑(n + 1) with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
Int.negSucc n |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | rfl | case h.negSucc
n : ℕ
hnp1 : ↑n + 1 = ↑(n + 1)
⊢ (match ↑(n + 1) with
| Int.ofNat n => Int.negOfNat n
| Int.negSucc n => ↑n + 1) =
Int.negSucc n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.neg_neg | [115, 9] | [132, 14] | simp | n : ℕ
⊢ ↑n + 1 = ↑(n + 1) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.zero_eq_mul | [136, 9] | [140, 26] | rw [eq_comm] | a b : ℤ
⊢ 0 = a * b ↔ a = 0 ∨ b = 0 | a b : ℤ
⊢ a * b = 0 ↔ a = 0 ∨ b = 0 |
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