22 lines
488 B
Text
22 lines
488 B
Text
import logic
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open eq.ops
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namespace experiment
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inductive nat : Type :=
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zero : nat,
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succ : nat → nat
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namespace nat
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definition add (x y : nat) : nat := nat.rec x (λn r, succ r) y
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infixl `+` := add
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definition mul (n m : nat) := nat.rec zero (fun m x, x + n) m
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infixl `*` := mul
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axiom mul_zero_right (n : nat) : n * zero = zero
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constant P : nat → Prop
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print "==========================="
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theorem tst (n : nat) (H : P (n * zero)) : P zero
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:= eq.subst (mul_zero_right _) H
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end nat
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exit
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