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Theorems · Theorem · order theory

IsAbsoluteValue.abv_eq_zero

∀ {S : Type u_5} [inst : Semiring S] [inst_1 : PartialOrder S] {R : Type u_6} [inst_2 : Semiring R] (abv : R → S)
  [IsAbsoluteValue abv] {x : R}, abv x = 0 ↔ x = 0
Defined in
Mathlib.Algebra.Order.AbsoluteValue.Basic
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
SemiringPartialOrderSemiringIsAbsoluteValue
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Around this declaration

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

CauSeq.const_limZero · cited by 6CauSeq.const_limZeroCauSeq.one_not_equiv_zero · cited by 1CauSeq.one_not_equiv_zeroSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderIsAbsoluteValue · cited by 160IsAbsoluteValueIsAbsoluteValue.abv_eq_zero' · cited by 1IsAbsoluteValue.abv_eq_ze…IsAbsoluteValue.abv_eq_zeroCITED BYCITES

Cites4

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Cited by2

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