Theorems · Theorem · commutative algebra

Valuation.one_apply_def

∀ {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), 1 x = if x = 0 then 0 else 1

Defined in

Mathlib.RingTheory.Valuation.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

RingLinearOrderedCommMonoidWithZeroNontrivialNoZeroDivisorsDecidablePred