Theorems · Theorem · commutative algebra
ValuativeRel.uniformizer_inv_le_iff
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] [inst_2 : ValuativeRel.IsDiscrete R]
[ValuativeRel.IsNontrivial R] {a : ValuativeRel.ValueGroupWithZero R}, (ValuativeRel.uniformizer R)⁻¹ ≤ a ↔ 1 < a- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.ValueGroupWithZerostatement and proof · cited by 86
- bot_lt_iff_ne_botproof · cited by 57
- ValuativeRel.IsNontrivialstatement and proof · cited by 12
- ValuativeRel.IsDiscretestatement and proof · cited by 10
- inv_lt_one₀proof · cited by 9
- inv_le_comm₀proof · cited by 8
- ValuativeRel.uniformizerstatement and proof · cited by 6
- ValuativeRel.uniformizer_posproof · cited by 2
- ValuativeRel.le_uniformizer_iffproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.