evalRealToEReal — Mathlib

Lean4
/-- Extension for the `positivity` tactic: cast from `ℝ` to `EReal`. -/
@[positivity Real.toEReal _]
def evalRealToEReal : PositivityExt where
  eval {u α} _zα _pα
    e := do
    match u, α, e with
    | 0, ~q(EReal), ~q(Real.toEReal $a) =>
      let ra ← core q(inferInstance) q(inferInstance) a
      assertInstancesCommute
      match ra with
      | .positive pa =>
        pure (.positive q(EReal.coe_pos.2 $pa))
      | .nonnegative pa =>
        pure (.nonnegative q(EReal.coe_nonneg.2 $pa))
      | .nonzero pa =>
        pure (.nonzero q(EReal.coe_ne_zero.2 $pa))
      | _ =>
        pure .none
    | _, _, _ =>
      throwError"not Real.toEReal"
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