Theorems · Theorem · commutative algebra
Valuation.RankOne.strictMono
∀ {R : Type u_1} {Γ₀ : Type u_2} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
[hv : v.RankOne], StrictMono ⇑(Valuation.RankOne.hom v)- Defined in
- Mathlib.RingTheory.Valuation.RankOne
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- NNRealstatement · cited by 4,310
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- Valuationstatement and proof · cited by 823
- StrictMonostatement · cited by 706
- MonoidWithZeroHomstatement · cited by 704
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.ValueGroup₀statement · cited by 166
Cited by10
Results whose statement or proof uses this declaration.
- Valuation.RankOne.exists_val_ltproof · cited by 1
- Valuation.norm_add_leproof · cited by 1
- Valued.toNormedField.norm_lt_one_iffproof · cited by 1
- Valuation.RankOne.zero_of_hom_zeroproof · cited by 1
- Valuation.norm_pos_iff_valuation_posproof · cited by 0
- Valued.toNormedField.norm_le_iffproof · cited by 0
- Valued.toNormedField.norm_le_one_iffproof · cited by 0
- Valued.toNormedField.norm_lt_iffproof · cited by 0
- Valued.toNormedField.one_le_norm_iffproof · cited by 0
- Valued.toNormedField.one_lt_norm_iffproof · cited by 0