lean2/tests/lean/run/eq13.lean

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
feat(library/init/logic): add 'arbitrary' It is identical to default, but it is opaque. That is, when we use 'arbitrary A', we cannot rely on the particular value selected. 2015-01-05 21:27:09 +00:00			`open nat`
test(tests/lean/run): add more overlapping patterns examples 2015-01-05 20:25:14 +00:00
			`definition f : nat → nat → nat,`
			`f _ 0 := 0,`
			`f 0 _ := 1,`
feat(library/init/logic): add 'arbitrary' It is identical to default, but it is opaque. That is, when we use 'arbitrary A', we cannot rely on the particular value selected. 2015-01-05 21:27:09 +00:00			`f _ _ := arbitrary nat`
test(tests/lean/run): add more overlapping patterns examples 2015-01-05 20:25:14 +00:00
			`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`

feat(library/init/logic): add 'arbitrary' It is identical to default, but it is opaque. That is, when we use 'arbitrary A', we cannot rely on the particular value selected. 2015-01-05 21:27:09 +00:00			`theorem f_succ_succ (a b : nat) : f (a+1) (b+1) = arbitrary nat :=`
test(tests/lean/run): add more overlapping patterns examples 2015-01-05 20:25:14 +00:00			`rfl`