Theorems · Definition · commutative algebra

Valuation.IsNontrivial.casesOn

{R : Type u_3} →
  {Γ₀ : Type u_4} →
    [inst : Ring R] →
      [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] →
        {v : Valuation R Γ₀} →
          {motive : v.IsNontrivial → Sort u} →
            (t : v.IsNontrivial) → ((exists_val_nontrivial : ∃ x, v x ≠ 0 ∧ v x ≠ 1) → motive ⋯) → motive t

Defined in

Mathlib.RingTheory.Valuation.Basic

Cited by

3 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext

Assumes

RingLinearOrderedCommMonoidWithZero