evalENNRealToEReal — Mathlib

Lean4
/-- Extension for the `positivity` tactic: cast from `ℝ≥0∞` to `EReal`. -/
@[positivity ENNReal.toEReal _]
def evalENNRealToEReal : PositivityExt where
  eval {u α} _zα _pα
    e := do
    match u, α, e with
    | 0, ~q(EReal), ~q(ENNReal.toEReal $a) =>
      let ra ← core q(inferInstance) q(inferInstance) a
      assertInstancesCommute
      match ra with
      | .positive pa =>
        pure (.positive q(EReal.coe_ennreal_pos.2 $pa))
      | .nonzero pa =>
        pure (.positive q(EReal.coe_ennreal_pos_iff_ne_zero.2 $pa))
      | _ =>
        pure (.nonnegative q(EReal.coe_ennreal_nonneg $a))
    | _, _, _ =>
      throwError"not ENNReal.toEReal"
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