evalERealToENNReal — Mathlib

Lean4
/-- Extension for the `positivity` tactic: projection from `EReal` to `ℝ≥0∞`.

We show that `EReal.toENNReal x` is positive whenever `x` is positive,
and it is nonnegative otherwise.
We cannot deduce any corollaries from `x ≠ 0`, since `EReal.toENNReal x = 0` for `x < 0`.
-/
@[positivity EReal.toENNReal _]
def evalERealToENNReal : PositivityExt where
  eval {u α} _zα _pα
    e := do
    match u, α, e with
    | 0, ~q(ENNReal), ~q(EReal.toENNReal $a) =>
      assertInstancesCommute
      match ← core q(inferInstance) q(inferInstance) a with
      | .positive pa =>
        pure (.positive q(EReal.toENNReal_pos_iff.2 $pa))
      | _ =>
        pure (.nonnegative q(zero_le $e))
    | _, _, _ =>
      throwError"not EReal.toENNReal"
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