Mathlib Map

Theorems · Theorem · order theory

IsAbsoluteValue.abv_pos

∀ {S : Type u_5} [inst : Semiring S] [inst_1 : PartialOrder S] {R : Type u_6} [inst_2 : Semiring R] (abv : R → S)
  [IsAbsoluteValue abv] {a : R}, 0 < abv a ↔ a ≠ 0
Defined in
Mathlib.Algebra.Order.AbsoluteValue.Basic
Cited by
4 results in Mathlib
Foundations
Depth 20 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.

Polynomial.tendsto_abv_eval₂_atTop · cited by 2Polynomial.tendsto_abv_ev…CauSeq.inv_mul_cancel · cited by 2CauSeq.inv_mul_cancelrat_inv_continuous_lemma · cited by 2rat_inv_continuous_lemmaCauSeq.mul_inv_cancel · cited by 1CauSeq.mul_inv_cancelSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderIsAbsoluteValue · cited by 160IsAbsoluteValueIsAbsoluteValue.toAbsoluteValue · cited by 12IsAbsoluteValue.toAbsolut…AbsoluteValue.pos_iff · cited by 6AbsoluteValue.pos_iffIsAbsoluteValue.abv_posCITED BYCITES

Cites5

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Cited by4

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