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Theorems · Theorem · commutative algebra

ValuativeRel.IsNontrivial.exists_lt_one

∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] [ValuativeRel.IsNontrivial R], ∃ γ, 0 < γ ∧ γ < 1
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
Cited by
1 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringValuativeRelValuativeRel.IsNontrivial
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ValuativeRel.uniformizer_pos · cited by 2ValuativeRel.uniformizer_…Semiring · cited by 13802SemiringValuativeRel · cited by 241ValuativeRelValuativeRel.ValueGroupWithZero · cited by 86ValuativeRel.ValueGroupWi…zero_lt_iff · cited by 29zero_lt_ifflt_or_lt_iff_ne · cited by 13lt_or_lt_iff_neValuativeRel.IsNontrivial · cited by 12ValuativeRel.IsNontrivialValuativeRel.IsNontrivial.condition · cited by 1IsNontrivial.conditionIsNontrivial.exists_lt_oneCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.