mk_eq_mk — Mathlib

English

The equality Mk a = Mk b is equivalent to the Archimedean domination both ways: ∃ m, |b| ≤ |a|^m and ∃ n, |a| ≤ |b|^n.

Русский

Ровно Mk a = Mk b эквивалентно существованию Archimedean доминирования в обе стороны: ∃ m, |b| ≤ |a|^m и ∃ n, |a| ≤ |b|^n.

LaTeX

$$$ mk\,a = mk\,b \iff (\exists m, |b| ≤ |a|^m) \land (\exists n, |a| ≤ |b|^n)$$$

Lean4

@[to_additive]
theorem mk_eq_mk {a b : M} : mk a = mk b ↔ (∃ m, |b|ₘ ≤ |a|ₘ ^ m) ∧ (∃ n, |a|ₘ ≤ |b|ₘ ^ n) :=
  by
  unfold mk toAntisymmetrization
  rw [Quotient.eq]
  rfl

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