13 lines
464 B
Text
13 lines
464 B
Text
open nat decidable
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definition has_decidable_eq : ∀ a b : nat, decidable (a = b),
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has_decidable_eq 0 0 := inl rfl,
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has_decidable_eq (a+1) 0 := inr (λ h, nat.no_confusion h),
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has_decidable_eq 0 (b+1) := inr (λ h, nat.no_confusion h),
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has_decidable_eq (a+1) (b+1) :=
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if H : a = b
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then inl (eq.rec_on H rfl)
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else inr (λ h : a+1 = b+1, nat.no_confusion h (λ e : a = b, absurd e H))
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check has_decidable_eq
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print definition has_decidable_eq
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