lean4-htt/doc/examples/Certora2022/ex23.lean
2022-11-21 17:02:28 -08:00

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/- split tactic -/
def f (x y z : Nat) : Nat :=
match x, y, z with
| 5, _, _ => y
| _, 5, _ => y
| _, _, 5 => y
| _, _, _ => 1
example : x ≠ 5 → y ≠ 5 → z ≠ 5 → z = w → f x y w = 1 := by
intros
simp [f]
split
. contradiction
. contradiction
. contradiction
. rfl
def g (xs ys : List Nat) : Nat :=
match xs, ys with
| [a, b], _ => a+b+1
| _, [b, c] => b+1
| _, _ => 1
example (xs ys : List Nat) (h : g xs ys = 0) : False := by
unfold g at h; split at h <;> simp_arith at h