Theorems · Theorem · commutative algebra
Valuation.integers_nontrivial
∀ {R : Type u} {Γ₀ : Type v} [inst : CommRing R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀),
Nontrivial ↥v.integer ↔ Nontrivial R- Defined in
- Mathlib.RingTheory.Valuation.Integers
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Nontrivialstatement · cited by 2,416
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.integerstatement · cited by 68
- Valuation.integer.integersproof · cited by 17
- Valuation.Integers.nontrivial_iffproof · cited by 2
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