evalDyckWordFirstReturn — Mathlib

Lean4

/-- Extension for the `positivity` tactic: `p.firstReturn` is positive if `p` is nonzero. -/
@[positivity DyckWord.firstReturn _]
def evalDyckWordFirstReturn : PositivityExt where
  eval {u α} _zα _pα
    e := do
    match u, α, e with
    | 0, ~q(ℕ), ~q(DyckWord.firstReturn $a) =>
      let ra ← core q(inferInstance) q(inferInstance) a
      assertInstancesCommute
      match ra with
      | .positive pa =>
        pure (.positive q(DyckWord.firstReturn_pos ($pa).ne'))
      | .nonzero pa =>
        pure (.positive q(DyckWord.firstReturn_pos $pa))
      | _ =>
        pure .none
    | _, _, _ =>
      throwError"not DyckWord.firstReturn"

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