26 lines
887 B
Text
26 lines
887 B
Text
section
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open tactic
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definition cases_refl (e : expr) : tactic :=
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cases e expr_list.nil; apply rfl
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definition cases_lst_refl : expr_list → tactic
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| cases_lst_refl expr_list.nil := apply rfl
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| cases_lst_refl (expr_list.cons a l) := cases a expr_list.nil; cases_lst_refl l
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-- Similar to cases_refl, but make sure the argument is not an arbitrary expression.
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definition eq_rec {A : Type} {a b : A} (e : a = b) : tactic :=
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cases e expr_list.nil; apply rfl
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end
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notation `cases_lst` l:(foldr `,` (h t, tactic.expr_list.cons h t) tactic.expr_list.nil) := cases_lst_refl l
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open prod
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theorem tst₁ (a : nat × nat) : (pr1 a, pr2 a) = a :=
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by cases_refl a
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theorem tst₂ (a b : nat × nat) (h₁ : pr₁ a = pr₁ b) (h₂ : pr₂ a = pr₂ b) : a = b :=
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by cases_lst a, b, h₁, h₂
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open nat
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theorem tst₃ (a b : nat) (h : a = b) : a + b = b + a :=
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by eq_rec h
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