lean2/tests/lean/run/eq13.lean

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Text

open nat
definition f : nat → nat → nat
| f _ 0 := 0
| f 0 _ := 1
| f _ _ := arbitrary nat
theorem f_zero_right : ∀ a, f a 0 = 0
| f_zero_right 0 := rfl
| f_zero_right (succ _) := rfl
theorem f_zero_succ (a : nat) : f 0 (a+1) = 1 :=
rfl
theorem f_succ_succ (a b : nat) : f (a+1) (b+1) = arbitrary nat :=
rfl