Theorems · Theorem · commutative algebra
Valuation.map_one
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀),
v 1 = 1- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.toMonoidWithZeroHomproof · cited by 16
- MonoidWithZeroHom.map_one'proof · cited by 3
Cited by17
Results whose statement or proof uses this declaration.
- Valuation.IsEquiv.eq_one_iff_eq_oneproof · cited by 5
- Valuation.Integers.dvd_of_leproof · cited by 4
- Valuation.Integers.one_of_isUnit'proof · cited by 3
- Valuation.Integers.isUnit_of_oneproof · cited by 2
- Valued.continuous_extensionproof · cited by 2
- Valuation.isEquiv_iff_val_eq_oneproof · cited by 2
- Valuation.map_one_add_of_ltproof · cited by 2
- Valuation.IsEquiv.le_one_iff_le_oneproof · cited by 2
- Valuation.IsEquiv.lt_one_iff_lt_oneproof · cited by 2
- AddValuation.map_oneproof · cited by 1
- Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRingproof · cited by 1
- ValuationSubring.valuation_unitproof · cited by 1