dd78012ddd
Although `HEq` was abbreviated as `≍` in #8503, many instances of the form `HEq x y` still remain. Therefore, I searched for occurrences of `HEq x y` using the regular expression `(?<![A-Za-z/@]|``)HEq(?![A-Za-z.])` and replaced as many as possible with the form `x ≍ y`.
27 lines
942 B
Text
27 lines
942 B
Text
theorem ex1 {α : Sort u} {a b : α} (h : a ≍ b) : a = b :=
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match h with
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| HEq.refl _ => rfl
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def ex2 {α : Sort u2} {a : α} {motive : {β : Sort u2} → β → Sort u1} (m : motive a) {β : Sort u2} {b : β} (h : a ≍ b) : motive b :=
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match h, m with
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| HEq.refl _, m => m
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def ex3 {α : Sort u} {a : α} {p : α → Sort v} {b : α} (h₁ : a ≍ b) (h₂ : p a) : p b :=
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match h₁, h₂ with
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| HEq.refl _, h₂ => h₂
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theorem ex4 {α β : Sort u} {a : α} {b : β} (h : a ≍ b) : b ≍ a :=
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match h with
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| HEq.refl _ => HEq.refl _
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theorem ex5 {α : Sort u} {a a' : α} (h : a = a') : a ≍ a' :=
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match h with
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| rfl => HEq.refl _
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theorem ex6 {α β : Sort u} (h : α = β) (a : α) : cast h a ≍ a :=
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match h with
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| rfl => HEq.refl _
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theorem ex7 {α β σ : Sort u} {a : α} {b : β} {c : σ} (h₁ : a ≍ b) (h₂ : b ≍ c) : a ≍ c :=
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match h₁, h₂ with
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| HEq.refl _, HEq.refl _ => HEq.refl _
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