evalNatCeil — Mathlib

Lean4
/-- Extension for the `positivity` tactic: `Nat.ceil` is positive if its input is. -/
@[positivity ⌈_⌉₊]
def evalNatCeil : PositivityExt where
  eval {u α} _zα _pα
    e := do
    match u, α, e with
    | 0, ~q(ℕ), ~q(@Nat.ceil $α' $ir $io $j $a) =>
      let _i ← synthInstanceQ q(LinearOrder $α')
      let _i ← synthInstanceQ q(IsStrictOrderedRing $α')
      assertInstancesCommute
      match ← core q(inferInstance) q(inferInstance) a with
      | .positive pa =>
        assertInstancesCommute
        pure (.positive q(nat_ceil_pos (α := $α') $pa))
      | _ =>
        pure .none
    | _, _, _ =>
      throwError"failed to match on Nat.ceil application"
Похожие утверждения