2015-01-27 19:22:14 +00:00
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open eq.ops
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inductive Nat : Type :=
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2015-02-26 01:00:10 +00:00
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zero : Nat |
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2015-01-27 19:22:14 +00:00
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succ : Nat → Nat
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namespace Nat
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definition pred (n : Nat) := Nat.rec zero (fun m x, m) n
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theorem pred_succ (n : Nat) : pred (succ n) = n := rfl
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2015-06-15 11:10:03 +00:00
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theorem succ.inj {n m : Nat} (H : succ n = succ m) : n = m
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2015-01-27 19:22:14 +00:00
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:= calc
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n = pred (succ n) : pred_succ n⁻¹
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... = pred (succ m) : {H}
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... = m : pred_succ m
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end Nat
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