Theorems · Theorem · order theory
AbsoluteValue.nonpos_iff
∀ {R : Type u_5} {S : Type u_6} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : PartialOrder S]
(abv : AbsoluteValue R S) {x : R}, abv x ≤ 0 ↔ x = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- SemiringSemiringPartialOrder
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- AbsoluteValuestatement and proof · cited by 363
- AbsoluteValue.nonnegproof · cited by 16
- AbsoluteValue.eq_zeroproof · cited by 5
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