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Theorems · Theorem · functional analysis

WithAbs.equivWithAbs_equiv_symm_apply

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} {x : R},
  (WithAbs.congr v w (RingEquiv.refl R)) ((WithAbs.equiv v).symm x) = (WithAbs.equiv w).symm x
Defined in
Mathlib.Analysis.Normed.Ring.WithAbs
Cited by
0 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Quot.sound
Assumes
SemiringPartialOrderSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderRingEquiv · cited by 1147RingEquivRingEquiv.symm · cited by 567RingEquiv.symmAbsoluteValue · cited by 363AbsoluteValueWithAbs · cited by 102WithAbsRingEquiv.refl · cited by 72RingEquiv.reflWithAbs.equiv · cited by 15WithAbs.equivWithAbs.congr · cited by 12WithAbs.congrWithAbs.equiv_symm_apply · cited by 5WithAbs.equiv_symm_applyWithAbs.equivWithAbs_equiv_sy…CITED BYCITES

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