Theorems · Theorem · commutative algebra
Valuation.IsEquiv.ofClass_eq_zero
∀ {R : Type u_3} {Γ₀ : Type u_4} {Γ'₀ : Type u_5} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀]
[inst_2 : LinearOrderedCommMonoidWithZero Γ'₀] {v₁ : Valuation R Γ₀} {v₂ : Valuation R Γ'₀},
v₁.IsEquiv v₂ → ∀ {r : R}, (MonoidWithZeroHom.ofClass v₁) r = 0 ↔ (MonoidWithZeroHom.ofClass v₂) r = 0- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- MonoidWithZeroHomstatement · cited by 704
- MonoidWithZeroHom.ofClassstatement · cited by 204
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.IsEquivstatement and proof · cited by 67
- Valuation.IsEquiv.eq_zeroproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- Valuation.IsEquiv.valueGroup₀Fun_specstatement · cited by 3
- Valuation.IsEquiv.orderMonoidIso_specproof · cited by 2
- Valuation.IsEquiv.orderMonoidIso_transproof · cited by 0
- Valuation.IsEquiv.orderMonoidIso_eq_reflproof · cited by 0