16 lines
293 B
Text
16 lines
293 B
Text
open nat
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definition f : nat → nat → nat
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| n 0 := 0
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| 0 n := 1
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| n m := arbitrary nat
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theorem f_zero_right : ∀ a, f a 0 = 0
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| 0 := rfl
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| (succ a) := rfl
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theorem f_zero_succ (a : nat) : f 0 (a+1) = 1 :=
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rfl
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theorem f_succ_succ (a b : nat) : f (a+1) (b+1) = arbitrary nat :=
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rfl
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