12 lines
377 B
Text
12 lines
377 B
Text
variables a b c d : Nat
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axiom H : a + (b + c) = a + (b + d)
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using Nat
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check add_succr a
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theorem mul_zerol2 (a : Nat) : 0 * a = 0
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:= induction_on a
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(have 0 * 0 = 0 : trivial)
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(λ (n : Nat) (iH : 0 * n = 0),
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calc 0 * (n + 1) = (0 * n) + 0 : mul_succr 0 n
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... = 0 + 0 : { iH }
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... = 0 : trivial)
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