13 lines
402 B
Text
13 lines
402 B
Text
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open nat
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lemma addz [simp] : ∀ a : nat, a + 0 = a := sorry
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lemma zadd [simp] : ∀ a : nat, 0 + a = a := sorry
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lemma adds [simp] : ∀ a b : nat, a + succ b = succ (a + b) := sorry
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lemma sadd [simp] : ∀ a b : nat, succ a + b = succ (a + b) := sorry
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definition comm : ∀ a b : nat, a + b = b + a
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| a 0 := by simp
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| a (succ n) :=
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assert a + n = n + a, from !comm,
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by simp
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