Theorems · Theorem · commutative algebra
Valuation.IsEquiv.symm
∀ {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 → v₂.IsEquiv v₁- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.IsEquivstatement and proof · cited by 67
Cited by7
Results whose statement or proof uses this declaration.
- Valuation.HasExtension.val_map_le_iffproof · cited by 5
- Valuation.IsEquiv.orderMonoidIso_specproof · cited by 2
- Valuation.IsEquiv.isNontrivial_iffproof · cited by 1
- RatFunc.valuation_isEquiv_infty_or_adicproof · cited by 1
- Valuation.mem_unitGroup_iffproof · cited by 0
- Valuation.IsEquiv.isTrivialOn_iffproof · cited by 0
- AddValuation.IsEquiv.symmproof · cited by 0