20 lines
421 B
Text
20 lines
421 B
Text
open bool nat
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definition is_eq (a b : nat) : bool :=
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nat.rec_on a
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(λ b, nat.cases_on b tt (λb₁, ff))
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(λ a₁ r₁ b, nat.cases_on b ff (λb₁, r₁ b₁))
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b
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example : is_eq 3 3 = tt :=
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rfl
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example : is_eq 3 5 = ff :=
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rfl
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theorem eq.to_is_eq (a b : nat) (H : a = b) : is_eq a b = tt :=
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have aux : is_eq a a = tt, from
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nat.rec_on a
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rfl
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(λ (a₁ : nat) (ih : is_eq a₁ a₁ = tt), ih),
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H ▸ aux
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