Theorems · Theorem · commutative algebra

Valuation.one_apply_of_ne_zero

∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] [inst_2 : Nontrivial R]
  [inst_3 : NoZeroDivisors R] [inst_4 : DecidablePred fun x => x = 0] {x : R}, x ≠ 0 → 1 x = 1

Defined in

Mathlib.RingTheory.Valuation.Basic

Cited by

3 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderedCommMonoidWithZeroNontrivialNoZeroDivisorsDecidablePred