Theorems · Theorem · commutative algebra
ValuationSubring.principalUnitGroup_le_principalUnitGroup
∀ {K : Type u} [inst : Field K] {A B : ValuationSubring K}, B.principalUnitGroup ≤ A.principalUnitGroup ↔ A ≤ B- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- not_ltproof · cited by 306
- inv_oneproof · cited by 301
- ValuationSubringstatement and proof · cited by 187
- add_sub_cancel_rightproof · cited by 187
- Units.mk0proof · cited by 181
- add_eq_zero_iff_eq_negproof · cited by 49
- inv_negproof · cited by 42
Cited by1
Results whose statement or proof uses this declaration.
- ValuationSubring.principalUnitGroupOrderEmbeddingproof · cited by 0