Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.embed_strictMono
∀ {R : Type u_2} {Γ : Type u_3} [inst : Ring R] [inst_1 : ValuativeRel R] [inst_2 : LinearOrderedCommGroupWithZero Γ]
(v : Valuation R Γ) [inst_3 : v.Compatible], StrictMono ⇑(ValuativeRel.ValueGroupWithZero.embed v)The map embed v is strictly monotone.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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
- Ringstatement and proof · cited by 7,463
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- map_mulproof · cited by 1,137
- map_oneproof · cited by 861
- Valuationstatement and proof · cited by 823
- StrictMonostatement · cited by 706
- MonoidWithZeroHomstatement · cited by 704
- div_oneproof · cited by 629
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- ValuativeRelstatement and proof · cited by 241
Cited by4
Results whose statement or proof uses this declaration.
- ValuativeExtension.mapValueGroupWithZero_strictMonoproof · cited by 1
- ValuativeRel.IsRankLeOne.of_compatible_mulArchimedeanproof · cited by 1
- ValuativeRel.IsDiscrete.of_compatible_withZeroMulIntproof · cited by 0
- ValuativeRel.ValueGroupWithZero.orderMonoidIso_strictMonoproof · cited by 0