Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.ind
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {motive : ValuativeRel.ValueGroupWithZero R → Prop},
(∀ (x : R) (y : ↥(ValuativeRel.posSubmonoid R)), motive (ValuativeRel.ValueGroupWithZero.mk x y)) →
∀ (t : ValuativeRel.ValueGroupWithZero R), motive t- Cited by
- 6 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Submonoidstatement · cited by 3,086
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.ValueGroupWithZerostatement and proof · cited by 86
- ValuativeRel.posSubmonoidstatement and proof · cited by 45
- ValuativeRel.ValueGroupWithZero.mkstatement and proof · cited by 25
- ValuativeRel.valueSetoidproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- ValuativeRel.exists_valuation_div_valuation_eqproof · cited by 2
- ValuativeRel.valuation_surjectiveproof · cited by 1
- ValuativeRel.ValueGroupWithZero.embedding_embed_valuation_eqproof · cited by 1
- ValuativeRel.isNontrivial_iff_isNontrivialproof · cited by 1
- ValuativeRel.ValueGroupWithZero.lift_mulproof · cited by 0
- ValuativeRel.ValueGroupWithZero.orderMonoidIso_embedproof · cited by 0