Theorems · Theorem · commutative algebra
ValuativeRel.isNontrivial_iff_nontrivial_units
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R],
ValuativeRel.IsNontrivial R ↔ Nontrivial (ValuativeRel.ValueGroupWithZero R)ˣ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringValuativeRel
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Unitsstatement and proof · cited by 2,804
- Nontrivialstatement and proof · cited by 2,416
- Units.valproof · cited by 1,966
- eq_or_neproof · cited by 1,117
- ValuativeRelstatement and proof · cited by 241
- Units.mk0proof · cited by 181
- ValuativeRel.ValueGroupWithZerostatement and proof · cited by 86
- ValuativeRel.IsNontrivialstatement and proof · cited by 12
- Nontrivial.casesOnproof · cited by 6
- ValuativeRel.IsNontrivial.casesOnproof · cited by 3
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