ordFrac_eq_div — Mathlib

English

The full equality of ordFrac with the division of ordMonoidWithZeroHom on a,b in the fraction field holds under hypotheses.

Русский

Полное равенство ordFrac и деление ordMonoidWithZeroHom на a,b в дробном поле сохраняется при предпосылках.

LaTeX

$$ordFrac R a = ordMonoidWithZeroHom R a, for elements a,b in the fraction field$$

Lean4

theorem ordFrac_eq_div (a : nonZeroDivisors R) (b : nonZeroDivisors R) :
    ordFrac R (IsLocalization.mk' K a.1 b) = ordMonoidWithZeroHom R a / ordMonoidWithZeroHom R b := by
  simp [ordFrac_eq_ord]

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