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Theorems · Theorem · field theory

AbsoluteValue.IsEquiv.eq_iff_eq

∀ {R : Type u_1} [inst : Semiring R] {S : Type u_2} [inst_1 : Semiring S] [inst_2 : PartialOrder S]
  {v w : AbsoluteValue R S}, v.IsEquiv w → ∀ {x y : R}, v x = v y ↔ w x = w y
Defined in
Mathlib.Analysis.AbsoluteValue.Equivalence
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
SemiringSemiringPartialOrder
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Around this declaration

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

AbsoluteValue.IsEquiv.eq_one_iff · cited by 3IsEquiv.eq_one_iffDFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderAbsoluteValue · cited by 363AbsoluteValueAbsoluteValue.IsEquiv · cited by 32AbsoluteValue.IsEquivIsEquiv.eq_iff_eqCITED BYCITES

Cites5

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Cited by1

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