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Theorems · Definition · commutative algebra

ValuativeRel.IsNontrivial.casesOn

{R : Type u_1} →
  [inst : Semiring R] →
    [inst_1 : ValuativeRel R] →
      {motive : ValuativeRel.IsNontrivial R → Sort u} →
        (t : ValuativeRel.IsNontrivial R) → ((condition : ∃ γ, γ ≠ 0 ∧ γ ≠ 1) → motive ⋯) → motive t
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
Cited by
3 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringValuativeRel
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ValuativeRel.isNontrivial_iff_isNontrivial · cited by 1ValuativeRel.isNontrivial…ValuativeRel.isNontrivial_iff_nontrivial_units · cited by 0ValuativeRel.isNontrivial…ValuativeRel.not_isNontrivial_of_trivialRel · cited by 0ValuativeRel.not_isNontri…Semiring · cited by 13802SemiringValuativeRel · cited by 241ValuativeRelValuativeRel.ValueGroupWithZero · cited by 86ValuativeRel.ValueGroupWi…ValuativeRel.IsNontrivial · cited by 12ValuativeRel.IsNontrivialIsNontrivial.casesOnCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.