archimedean_stratum — Mathlib

English

Same as the previous: a nonzero a in the stratum c yields ArchimedeanClass.mk a = c.

Русский

То же самое: не ноль a в слое c даёт ArchimedeanClass.mk a = c.

LaTeX

$$$ a \in u.stratum c \land a \neq 0 \Rightarrow \operatorname{ArchimedeanClass.mk} a = c $$$

Lean4

instance archimedean_stratum : Archimedean (u.stratum c) :=
  by
  apply archimedean_of_mk_eq_mk
  intro a ha b hb
  suffices ArchimedeanClass.mk a.val = ArchimedeanClass.mk b.val
    by
    rw [mk_eq_mk] at this ⊢
    exact this
  rw [u.archimedeanClassMk_of_mem_stratum a.prop (by simpa using ha)]
  rw [u.archimedeanClassMk_of_mem_stratum b.prop (by simpa using hb)]

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