instEstimatorNatHAddThunkProd — Mathlib

English

For two thunk Nat estimators, there is a product estimator data for their HAdd with bounds on Nat addition.

Русский

Для двух thunk Nat существaет оцениватель-данные для их HAdd с пределами на сложение Nat.

LaTeX

$$instEstimatorNatHAddThunkProd a b εa εb : Estimator (a + b) (εa × εb) with bound e := bound a e.1 + bound b e.2 and improve as in the general HAdd case$$

Lean4

instance (a b : Thunk ℕ) {εa εb : Type*} [Estimator a εa] [Estimator b εb] : Estimator (a + b) (εa × εb)
    where
  bound_le e := Nat.add_le_add (Estimator.bound_le e.1) (Estimator.bound_le e.2)
  improve_spec
    e := by
    dsimp
    have s₁ := Estimator.improve_spec (a := a) e.1
    have s₂ := Estimator.improve_spec (a := b) e.2
    grind

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