English
If two erased elements have equal out-values, then they are equal; mapping through Erased preserves the call structure.
Русский
Если два стертых элемента имеют одинаковое значение out, то они равны; отображение через Erased сохраняет структуру вызова.
LaTeX
$$$\\forall a,b:\\mathrm{Erased}\\,\\alpha,\\ a.\\mathrm{out} = b.\\mathrm{out} \\Rightarrow a = b$$$
Lean4
theorem valid : ValidFinite emin 0 :=
⟨by
rw [add_sub_assoc]
apply le_add_of_nonneg_right
apply sub_nonneg_of_le
apply Int.ofNat_le_ofNat_of_le
exact C.precPos,
suffices prec ≤ 2 * emax by
rw [← Int.ofNat_le] at this
rw [← sub_nonneg] at *
simp only [emin, emax] at *
cutsat
le_trans C.precMax (Nat.le_mul_of_pos_left _ Nat.zero_lt_two),
by (simp [sub_eq_add_neg, Int.ofNat_zero_le])⟩
