Datasets:
internlm
/
Lean-Github

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https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_subst [right, right_2]
case right.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : ¬T snd_1 snd right : snd = snd_1 ⊢ ¬(S fst_1 fst_1 ∨ T snd_1 snd_1)
case right.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left_1 left_3 : ¬T snd_1 snd_1 left left_2 : ¬S fst_1 fst_1 ⊢ ¬(S fst_1 fst_1 ∨ T snd_1 snd_1)
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [not_false_eq_true, or_self]
case right.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left_1 left_3 : ¬T snd_1 snd_1 left left_2 : ¬S fst_1 fst_1 ⊢ ¬(S fst_1 fst_1 ∨ T snd_1 snd_1)
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
with_reducible aesop_destruct_products
case right.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 ⊢ ¬(S fst_1 fst_1 ∨ T snd_1 snd_1)
case right.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : ¬T snd_1 snd right : snd = snd_1 ⊢ ¬(S fst_1 fst_1 ∨ T snd_1 snd_1)
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_destruct_products
case right.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 ⊢ ¬(S fst_1 fst_1 ∨ T snd_1 snd_1)
case right.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : ¬T snd_1 snd right : snd = snd_1 ⊢ ¬(S fst_1 fst_1 ∨ T snd_1 snd_1)
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [and_false, or_false, and_self, or_true, not_true_eq_false, not_false_eq_true, forall_true_left, and_true, false_or]
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ fst = fst_1 ∧ snd = snd_1 ∨ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ (S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1) ∨ (S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1)
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
unhygienic with_reducible aesop_destruct_products
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_subst right_2
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left_1 : ¬T snd snd_1 left_3 : T snd_1 snd right : ¬snd = snd_1 left left_2 : ¬S fst_1 fst_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [not_false_eq_true]
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left_1 : ¬T snd snd_1 left_3 : T snd_1 snd right : ¬snd = snd_1 left left_2 : ¬S fst_1 fst_1 ⊢ ¬S fst_1 fst_1
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
with_reducible aesop_destruct_products
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_destruct_products
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
case right.inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [and_self, or_true, not_true_eq_false, and_false, or_false, not_false_eq_true, forall_true_left, and_true, false_and, true_and, false_or]
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : T snd snd_1 ∧ ¬T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ fst = fst_1 ∧ snd = snd_1 ∨ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ (S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1) ∨ (S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1)
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : T snd snd_1 ∧ ¬T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
unhygienic with_reducible aesop_destruct_products
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : T snd snd_1 ∧ ¬T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : ¬T snd_1 snd right : ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_subst right_2
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : ¬T snd_1 snd right : ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left_1 : T snd snd_1 left_3 : ¬T snd_1 snd right : ¬snd = snd_1 left left_2 : ¬S fst_1 fst_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [not_false_eq_true]
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left_1 : T snd snd_1 left_3 : ¬T snd_1 snd right : ¬snd = snd_1 left left_2 : ¬S fst_1 fst_1 ⊢ ¬S fst_1 fst_1
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
with_reducible aesop_destruct_products
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : T snd snd_1 ∧ ¬T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : ¬T snd_1 snd right : ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_destruct_products
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ ¬S fst_1 fst ∧ fst = fst_1 h_1 : T snd snd_1 ∧ ¬T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
case right.inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : ¬S fst fst_1 left_1 : T snd snd_1 left_2 : ¬S fst_1 fst right_2 : fst = fst_1 left_3 : ¬T snd_1 snd right : ¬snd = snd_1 ⊢ ¬S fst_1 fst_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [false_and, or_self, not_false_eq_true, true_or, not_true_eq_false, and_true, and_self, and_false, IsEmpty.forall_iff, or_false, or_true]
case right.inr.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 h : ¬S fst fst_1 ∧ S fst_1 fst ∧ ¬fst = fst_1 ⊢ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ fst = fst_1 ∧ snd = snd_1 ∨ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ (S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1) ∨ (S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1)
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [false_and, or_false, not_true_eq_false, false_or, not_and, and_true, and_false, and_self, IsEmpty.forall_iff, true_and]
case right.inr.inl.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 ⊢ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ fst = fst_1 ∧ snd = snd_1 ∨ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ (S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1) ∨ (S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1)
case right.inr.inl.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 ⊢ fst_1 = fst → ¬T snd_1 snd_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
intro a
case right.inr.inl.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 ⊢ fst_1 = fst → ¬T snd_1 snd_1
case right.inr.inl.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 a : fst_1 = fst ⊢ ¬T snd_1 snd_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_subst a
case right.inr.inl.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 a : fst_1 = fst ⊢ ¬T snd_1 snd_1
case right.inr.inl.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd snd_1 : β fst_2 : α snd_2 : β h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 h : S fst fst ∧ ¬S fst fst ∧ ¬fst = fst ⊢ ¬T snd_1 snd_1
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [not_true_eq_false, and_false]
case right.inr.inl.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd snd_1 : β fst_2 : α snd_2 : β h_1 : ¬T snd snd_1 ∧ ¬T snd_1 snd ∧ snd = snd_1 h : S fst fst ∧ ¬S fst fst ∧ ¬fst = fst ⊢ ¬T snd_1 snd_1
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [and_self, or_self, not_false_eq_true, and_true, true_or, not_true_eq_false, and_false, IsEmpty.forall_iff, or_false, or_true]
case right.inr.inr.inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ S fst_1 fst ∧ ¬fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ fst = fst_1 ∧ snd = snd_1 ∨ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ (S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1) ∨ (S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1)
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [and_true, or_self, not_false_eq_true, and_false, or_false, not_true_eq_false, and_self, IsEmpty.forall_iff, or_true]
case right.inr.inr.inl.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : ¬S fst fst_1 ∧ S fst_1 fst ∧ ¬fst = fst_1 h_1 : T snd snd_1 ∧ ¬T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ fst = fst_1 ∧ snd = snd_1 ∨ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ (S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1) ∨ (S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1)
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [and_self, or_false, not_true_eq_false, and_true, false_or, and_false, IsEmpty.forall_iff, false_and, true_and]
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ fst = fst_1 ∧ snd = snd_1 ∨ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ (S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1) ∨ (S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1)
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬fst_1 = fst
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
unhygienic with_reducible aesop_destruct_products
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬fst_1 = fst
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : ¬fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ ¬fst_1 = fst
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
apply Aesop.BuiltinRules.not_intro
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : ¬fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ ¬fst_1 = fst
case right.inr.inr.inr.inl.h α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : ¬fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ fst_1 = fst → False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
intro a
case right.inr.inr.inr.inl.h α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : ¬fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ fst_1 = fst → False
case right.inr.inr.inr.inl.h α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : ¬fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 a : fst_1 = fst ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_subst a
case right.inr.inr.inr.inl.h α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : ¬fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 a : fst_1 = fst ⊢ False
case right.inr.inr.inr.inl.h α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd snd_1 : β fst_2 : α snd_2 : β left_1 : ¬T snd snd_1 left_3 : T snd_1 snd right : ¬snd = snd_1 left : S fst fst left_2 : ¬S fst fst right_2 : ¬fst = fst ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only
case right.inr.inr.inr.inl.h α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd snd_1 : β fst_2 : α snd_2 : β left_1 : ¬T snd snd_1 left_3 : T snd_1 snd right : ¬snd = snd_1 left : S fst fst left_2 : ¬S fst fst right_2 : ¬fst = fst ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
with_reducible aesop_destruct_products
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬fst_1 = fst
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : ¬fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ ¬fst_1 = fst
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
aesop_destruct_products
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 h_1 : ¬T snd snd_1 ∧ T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬fst_1 = fst
case right.inr.inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β left : S fst fst_1 left_1 : ¬T snd snd_1 left_2 : ¬S fst_1 fst right_2 : ¬fst = fst_1 left_3 : T snd_1 snd right : ¬snd = snd_1 ⊢ ¬fst_1 = fst
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_strict_order
[524, 1]
[599, 37]
simp_all only [and_true, or_false, not_true_eq_false, and_false, or_self, not_false_eq_true, and_self, IsEmpty.forall_iff, or_true]
case right.inr.inr.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝ : DecidableRel S inst : DecidableRel T inst_1 : DecidableEq α inst_2 : DecidableEq β fst : α snd : β fst_1 : α snd_1 : β fst_2 : α snd_2 : β h : S fst fst_1 ∧ ¬S fst_1 fst ∧ ¬fst = fst_1 h_1 : T snd snd_1 ∧ ¬T snd_1 snd ∧ ¬snd = snd_1 ⊢ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ fst = fst_1 ∧ snd = snd_1 ∨ ¬(S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ (S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1) ∨ (S fst fst_1 ∨ fst = fst_1 ∧ T snd snd_1) ∧ ¬(S fst_1 fst ∨ fst_1 = fst ∧ T snd_1 snd) ∧ (fst = fst_1 → ¬snd = snd_1)
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
intro hwo
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β ⊢ ¬WeakOrder (R5 S T)
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : WeakOrder (R5 S T) ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
rw [WeakOrder] at hwo
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : WeakOrder (R5 S T) ⊢ False
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
have hf := hwo.2
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a ⊢ False
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a hf : ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
have p : α × β := Classical.choice Prod.Nonempty
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a hf : ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a ⊢ False
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a hf : ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
specialize hf p p
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a hf : ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β ⊢ False
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hf : R5 S T p p ∨ R5 S T p p ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
simp [R5] at hf
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hf : R5 S T p p ∨ R5 S T p p ⊢ False
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hf : S p.1 p.1 ∨ T p.2 p.2 ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
rcases hf with (hS1 | hT1)
α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hf : S p.1 p.1 ∨ T p.2 p.2 ⊢ False
case inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 ⊢ False case inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
rcases hS.trich p.1 p.1 with (hS2 | hS3 | hS4)
case inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 ⊢ False
case inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 hS2 : ¬S p.1 p.1 ∧ ¬S p.1 p.1 ∧ p.1 = p.1 ⊢ False case inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 hS3 : ¬S p.1 p.1 ∧ S p.1 p.1 ∧ ¬p.1 = p.1 ⊢ False case inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 hS4 : S p.1 p.1 ∧ ¬S p.1 p.1 ∧ ¬p.1 = p.1 ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
exact hS2.left hS1
case inl.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 hS2 : ¬S p.1 p.1 ∧ ¬S p.1 p.1 ∧ p.1 = p.1 ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
exact hS3.left hS1
case inl.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 hS3 : ¬S p.1 p.1 ∧ S p.1 p.1 ∧ ¬p.1 = p.1 ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
have := hS4.right.right
case inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 hS4 : S p.1 p.1 ∧ ¬S p.1 p.1 ∧ ¬p.1 = p.1 ⊢ False
case inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 hS4 : S p.1 p.1 ∧ ¬S p.1 p.1 ∧ ¬p.1 = p.1 this : ¬p.1 = p.1 ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
contradiction
case inl.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hS1 : S p.1 p.1 hS4 : S p.1 p.1 ∧ ¬S p.1 p.1 ∧ ¬p.1 = p.1 this : ¬p.1 = p.1 ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
rcases hT.trich p.2 p.2 with (hT2 | hT3 | hT4)
case inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 ⊢ False
case inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 hT2 : ¬T p.2 p.2 ∧ ¬T p.2 p.2 ∧ p.2 = p.2 ⊢ False case inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 hT3 : ¬T p.2 p.2 ∧ T p.2 p.2 ∧ ¬p.2 = p.2 ⊢ False case inr.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 hT4 : T p.2 p.2 ∧ ¬T p.2 p.2 ∧ ¬p.2 = p.2 ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
exact hT2.left hT1
case inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 hT2 : ¬T p.2 p.2 ∧ ¬T p.2 p.2 ∧ p.2 = p.2 ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
exact hT3.left hT1
case inr.inr.inl α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 hT3 : ¬T p.2 p.2 ∧ T p.2 p.2 ∧ ¬p.2 = p.2 ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
have := hT4.right.right
case inr.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 hT4 : T p.2 p.2 ∧ ¬T p.2 p.2 ∧ ¬p.2 = p.2 ⊢ False
case inr.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 hT4 : T p.2 p.2 ∧ ¬T p.2 p.2 ∧ ¬p.2 = p.2 this : ¬p.2 = p.2 ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
r5_not_weak_order
[639, 1]
[669, 20]
contradiction
case inr.inr.inr α β : Type S : α → α → Prop T : β → β → Prop hS : CStrictOrder S hT : CStrictOrder T inst✝⁵ : DecidableRel S inst✝⁴ : DecidableRel T inst✝³ : DecidableEq α inst✝² : DecidableEq β inst✝¹ : Nonempty α inst✝ : Nonempty β hwo : PartialOrder' (R5 S T) ∧ ∀ (a b : α × β), R5 S T a b ∨ R5 S T b a p : α × β hT1 : T p.2 p.2 hT4 : T p.2 p.2 ∧ ¬T p.2 p.2 ∧ ¬p.2 = p.2 this : ¬p.2 = p.2 ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
simp
α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α ⊢ R5' p [] ↔ False
α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α ⊢ ¬R5' p []
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
intro hr
α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α ⊢ ¬R5' p []
α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
rw [R5'] at hr
α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] ⊢ False
α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : False ⊢ False case x_1 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] ⊢ p = [] → False case x_2 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] ⊢ p = [] → False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
exact hr
α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : False ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
intro heq
case x_1 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] ⊢ p = [] → False
case x_1 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] heq : p = [] ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
rw [heq] at hr
case x_1 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] heq : p = [] ⊢ False
case x_1 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' [] [] heq : p = [] ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
rw [R5'] at hr
case x_1 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' [] [] heq : p = [] ⊢ False
case x_1 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : False heq : p = [] ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
exact hr
case x_1 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : False heq : p = [] ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
intro heq
case x_2 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] ⊢ p = [] → False
case x_2 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] heq : p = [] ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
rw [heq] at hr
case x_2 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' p [] heq : p = [] ⊢ False
case x_2 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' [] [] heq : p = [] ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
rw [R5'] at hr
case x_2 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : R5' [] [] heq : p = [] ⊢ False
case x_2 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : False heq : p = [] ⊢ False
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex6.lean
R5'_false
[688, 1]
[708, 13]
exact hr
case x_2 α : Type hlt : LT α inst✝² : CStrictOrder LT.lt inst✝¹ : DecidableRel LT.lt inst✝ : DecidableEq α p : List α hr : False heq : p = [] ⊢ False
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_union
[6, 1]
[20, 12]
intros x hx
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I ⊢ ⋃ j ∈ J, A j ⊆ ⋃ i ∈ I, A i
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β hx : x ∈ ⋃ j ∈ J, A j ⊢ x ∈ ⋃ i ∈ I, A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_union
[6, 1]
[20, 12]
simp only [Set.mem_iUnion, exists_prop]
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β hx : x ∈ ⋃ j ∈ J, A j ⊢ x ∈ ⋃ i ∈ I, A i
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β hx : x ∈ ⋃ j ∈ J, A j ⊢ ∃ i ∈ I, x ∈ A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_union
[6, 1]
[20, 12]
simp only [Set.mem_iUnion, exists_prop] at hx
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β hx : x ∈ ⋃ j ∈ J, A j ⊢ ∃ i ∈ I, x ∈ A i
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β hx : ∃ i ∈ J, x ∈ A i ⊢ ∃ i ∈ I, x ∈ A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_union
[6, 1]
[20, 12]
rcases hx with ⟨j, ⟨hj, hxj⟩⟩
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β hx : ∃ i ∈ J, x ∈ A i ⊢ ∃ i ∈ I, x ∈ A i
case intro.intro α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ ∃ i ∈ I, x ∈ A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_union
[6, 1]
[20, 12]
use j
case intro.intro α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ ∃ i ∈ I, x ∈ A i
case h α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ j ∈ I ∧ x ∈ A j
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_union
[6, 1]
[20, 12]
constructor
case h α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ j ∈ I ∧ x ∈ A j
case h.left α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ j ∈ I case h.right α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ x ∈ A j
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_union
[6, 1]
[20, 12]
exact hsub hj
case h.left α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ j ∈ I case h.right α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ x ∈ A j
case h.right α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ x ∈ A j
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_union
[6, 1]
[20, 12]
exact hxj
case h.right α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : β j : α hj : j ∈ J hxj : x ∈ A j ⊢ x ∈ A j
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_not_inter
[22, 1]
[39, 60]
use ℕ
⊢ ∃ α β J I A, J ⊆ I ∧ ¬⋂ j ∈ J, A j ⊆ ⋂ i ∈ I, A i
case h ⊢ ∃ β J I A, J ⊆ I ∧ ¬⋂ j ∈ J, A j ⊆ ⋂ i ∈ I, A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_not_inter
[22, 1]
[39, 60]
use ℕ
case h ⊢ ∃ β J I A, J ⊆ I ∧ ¬⋂ j ∈ J, A j ⊆ ⋂ i ∈ I, A i
case h ⊢ ∃ J I A, J ⊆ I ∧ ¬⋂ j ∈ J, A j ⊆ ⋂ i ∈ I, A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_not_inter
[22, 1]
[39, 60]
use {1}
case h ⊢ ∃ J I A, J ⊆ I ∧ ¬⋂ j ∈ J, A j ⊆ ⋂ i ∈ I, A i
case h ⊢ ∃ I A, {1} ⊆ I ∧ ¬⋂ j ∈ {1}, A j ⊆ ⋂ i ∈ I, A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_not_inter
[22, 1]
[39, 60]
use {1, 2}
case h ⊢ ∃ I A, {1} ⊆ I ∧ ¬⋂ j ∈ {1}, A j ⊆ ⋂ i ∈ I, A i
case h ⊢ ∃ A, {1} ⊆ {1, 2} ∧ ¬⋂ j ∈ {1}, A j ⊆ ⋂ i ∈ {1, 2}, A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_not_inter
[22, 1]
[39, 60]
let A := λ n : ℕ => ({0, n} : Set ℕ)
case h ⊢ ∃ A, {1} ⊆ {1, 2} ∧ ¬⋂ j ∈ {1}, A j ⊆ ⋂ i ∈ {1, 2}, A i
case h A : ℕ → Set ℕ := fun n => {0, n} ⊢ ∃ A, {1} ⊆ {1, 2} ∧ ¬⋂ j ∈ {1}, A j ⊆ ⋂ i ∈ {1, 2}, A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_not_inter
[22, 1]
[39, 60]
use A
case h A : ℕ → Set ℕ := fun n => {0, n} ⊢ ∃ A, {1} ⊆ {1, 2} ∧ ¬⋂ j ∈ {1}, A j ⊆ ⋂ i ∈ {1, 2}, A i
case h A : ℕ → Set ℕ := fun n => {0, n} ⊢ {1} ⊆ {1, 2} ∧ ¬⋂ j ∈ {1}, A j ⊆ ⋂ i ∈ {1, 2}, A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_not_inter
[22, 1]
[39, 60]
simp only [Set.mem_singleton_iff, OfNat.one_ne_ofNat, Set.singleton_subset_iff, Set.mem_insert_iff, or_false, Set.iInter_iInter_eq_left, Set.iInter_iInter_eq_or_left, Set.subset_inter_iff, not_false_eq_true, Set.insert_subset_insert_iff, Set.subset_singleton_iff, imp_self, forall_const, forall_eq, and_false, and_self]
case h A : ℕ → Set ℕ := fun n => {0, n} ⊢ {1} ⊆ {1, 2} ∧ ¬⋂ j ∈ {1}, A j ⊆ ⋂ i ∈ {1, 2}, A i
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_inter_rev
[42, 1]
[53, 21]
simp only [Set.subset_iInter_iff]
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I ⊢ ⋂ i ∈ I, A i ⊆ ⋂ j ∈ J, A j
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I ⊢ ∀ i ∈ J, ⋂ i ∈ I, A i ⊆ A i
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_inter_rev
[42, 1]
[53, 21]
intros x hx b hb
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I ⊢ ∀ i ∈ J, ⋂ i ∈ I, A i ⊆ A i
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : α hx : x ∈ J b : β hb : b ∈ ⋂ i ∈ I, A i ⊢ b ∈ A x
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_inter_rev
[42, 1]
[53, 21]
simp at hb
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : α hx : x ∈ J b : β hb : b ∈ ⋂ i ∈ I, A i ⊢ b ∈ A x
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : α hx : x ∈ J b : β hb : ∀ i ∈ I, b ∈ A i ⊢ b ∈ A x
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_inter_rev
[42, 1]
[53, 21]
specialize hb x
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : α hx : x ∈ J b : β hb : ∀ i ∈ I, b ∈ A i ⊢ b ∈ A x
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : α hx : x ∈ J b : β hb : x ∈ I → b ∈ A x ⊢ b ∈ A x
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
idx_set_inter_rev
[42, 1]
[53, 21]
exact hb (hsub hx)
α β : Type I J : Set α A : α → Set β hsub : J ⊆ I x : α hx : x ∈ J b : β hb : x ∈ I → b ∈ A x ⊢ b ∈ A x
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
sq_diophantine
[57, 1]
[66, 10]
intro h
x y : ℝ ⊢ x ^ 2 + 5 * y = y ^ 2 + 5 * x → x = y ∨ x + y = 5
x y : ℝ h : x ^ 2 + 5 * y = y ^ 2 + 5 * x ⊢ x = y ∨ x + y = 5
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
sq_diophantine
[57, 1]
[66, 10]
apply_fun (λ eq => eq - 5 * y - y ^ 2) at h
x y : ℝ h : x ^ 2 + 5 * y = y ^ 2 + 5 * x ⊢ x = y ∨ x + y = 5
x y : ℝ h : x ^ 2 + 5 * y - 5 * y - y ^ 2 = y ^ 2 + 5 * x - 5 * y - y ^ 2 ⊢ x = y ∨ x + y = 5
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
sq_diophantine
[57, 1]
[66, 10]
ring_nf at h
x y : ℝ h : x ^ 2 + 5 * y - 5 * y - y ^ 2 = y ^ 2 + 5 * x - 5 * y - y ^ 2 ⊢ x = y ∨ x + y = 5
x y : ℝ h : x ^ 2 - y ^ 2 = x * 5 - y * 5 ⊢ x = y ∨ x + y = 5
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
sq_diophantine
[57, 1]
[66, 10]
rw [sq_sub_sq, ←mul_sub_right_distrib, mul_comm] at h
x y : ℝ h : x ^ 2 - y ^ 2 = x * 5 - y * 5 ⊢ x = y ∨ x + y = 5
x y : ℝ h : (x - y) * (x + y) = (x - y) * 5 ⊢ x = y ∨ x + y = 5
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
sq_diophantine
[57, 1]
[66, 10]
rw [mul_eq_mul_left_iff, sub_eq_zero, or_comm] at h
x y : ℝ h : (x - y) * (x + y) = (x - y) * 5 ⊢ x = y ∨ x + y = 5
x y : ℝ h : x = y ∨ x + y = 5 ⊢ x = y ∨ x + y = 5
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex2.lean
sq_diophantine
[57, 1]
[66, 10]
exact h
x y : ℝ h : x = y ∨ x + y = 5 ⊢ x = y ∨ x + y = 5
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
ext x
⊢ {x | x ^ 2 = 17} = {Real.sqrt 17, -Real.sqrt 17}
case h x : ℝ ⊢ x ∈ {x | x ^ 2 = 17} ↔ x ∈ {Real.sqrt 17, -Real.sqrt 17}
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
simp
case h x : ℝ ⊢ x ∈ {x | x ^ 2 = 17} ↔ x ∈ {Real.sqrt 17, -Real.sqrt 17}
case h x : ℝ ⊢ x ^ 2 = 17 ↔ x = Real.sqrt 17 ∨ x = -Real.sqrt 17
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
constructor
case h x : ℝ ⊢ x ^ 2 = 17 ↔ x = Real.sqrt 17 ∨ x = -Real.sqrt 17
case h.mp x : ℝ ⊢ x ^ 2 = 17 → x = Real.sqrt 17 ∨ x = -Real.sqrt 17 case h.mpr x : ℝ ⊢ x = Real.sqrt 17 ∨ x = -Real.sqrt 17 → x ^ 2 = 17
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
intro hsq
case h.mp x : ℝ ⊢ x ^ 2 = 17 → x = Real.sqrt 17 ∨ x = -Real.sqrt 17
case h.mp x : ℝ hsq : x ^ 2 = 17 ⊢ x = Real.sqrt 17 ∨ x = -Real.sqrt 17
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
apply_fun (λ eq => Real.sqrt eq) at hsq
case h.mp x : ℝ hsq : x ^ 2 = 17 ⊢ x = Real.sqrt 17 ∨ x = -Real.sqrt 17
case h.mp x : ℝ hsq : Real.sqrt (x ^ 2) = Real.sqrt 17 ⊢ x = Real.sqrt 17 ∨ x = -Real.sqrt 17
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
rw [Real.sqrt_sq_eq_abs] at hsq
case h.mp x : ℝ hsq : Real.sqrt (x ^ 2) = Real.sqrt 17 ⊢ x = Real.sqrt 17 ∨ x = -Real.sqrt 17
case h.mp x : ℝ hsq : |x| = Real.sqrt 17 ⊢ x = Real.sqrt 17 ∨ x = -Real.sqrt 17
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
exact eq_or_eq_neg_of_abs_eq hsq
case h.mp x : ℝ hsq : |x| = Real.sqrt 17 ⊢ x = Real.sqrt 17 ∨ x = -Real.sqrt 17
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
intro hor
case h.mpr x : ℝ ⊢ x = Real.sqrt 17 ∨ x = -Real.sqrt 17 → x ^ 2 = 17
case h.mpr x : ℝ hor : x = Real.sqrt 17 ∨ x = -Real.sqrt 17 ⊢ x ^ 2 = 17
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
rcases hor with (hpos | hneg)
case h.mpr x : ℝ hor : x = Real.sqrt 17 ∨ x = -Real.sqrt 17 ⊢ x ^ 2 = 17
case h.mpr.inl x : ℝ hpos : x = Real.sqrt 17 ⊢ x ^ 2 = 17 case h.mpr.inr x : ℝ hneg : x = -Real.sqrt 17 ⊢ x ^ 2 = 17
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
rw [hpos]
case h.mpr.inl x : ℝ hpos : x = Real.sqrt 17 ⊢ x ^ 2 = 17
case h.mpr.inl x : ℝ hpos : x = Real.sqrt 17 ⊢ Real.sqrt 17 ^ 2 = 17
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
exact Real.sq_sqrt (by norm_num)
case h.mpr.inl x : ℝ hpos : x = Real.sqrt 17 ⊢ Real.sqrt 17 ^ 2 = 17
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
norm_num
x : ℝ hpos : x = Real.sqrt 17 ⊢ 0 ≤ 17
no goals
https://github.com/aronerben/lean4-playground.git
5efced915ecee24cd723d28d00aa63f9c7ea0a9c
meetings/ex1.lean
sqrt17
[11, 1]
[25, 39]
rw [hneg, neg_sq]
case h.mpr.inr x : ℝ hneg : x = -Real.sqrt 17 ⊢ x ^ 2 = 17
case h.mpr.inr x : ℝ hneg : x = -Real.sqrt 17 ⊢ Real.sqrt 17 ^ 2 = 17