lean2/tests/lean/run/eq4.lean

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open nat
definition half : nat → nat,
half 0 := 0,
half 1 := 0,
half (x+2) := half x + 1
theorem half0 : half 0 = 0 :=
rfl
theorem half1 : half 1 = 0 :=
rfl
theorem half_succ_succ (a : nat) : half (a + 2) = half a + 1 :=
rfl
example : half 5 = 2 :=
rfl
example : half 8 = 4 :=
rfl