Theorems · Definition · functional analysis

WithAbs.equivWithAbs

Deprecated since 2026-03-02Mathlib marks this declaration as deprecated.

{R : Type u_1} →
  {S : Type u_2} →
    [inst : Semiring S] →
      [inst_1 : PartialOrder S] → [inst_2 : Semiring R] → (v w : AbsoluteValue R S) → WithAbs v ≃+* WithAbs w

The canonical (semiring) equivalence between WithAbs v and WithAbs w, for any two absolute values v and w on R.

Defined in: Mathlib.Analysis.Normed.Ring.WithAbs
Cited by: 0 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Quot.sound
Assumes: Semiring PartialOrder Semiring

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Semiringstatement and proof · cited by 13,802
PartialOrderstatement and proof · cited by 6,410
RingEquivstatement · cited by 1,147
AbsoluteValuestatement and proof · cited by 363
WithAbsstatement · cited by 102
RingEquiv.reflproof · cited by 72
WithAbs.congrproof · cited by 12

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