Theorems · Theorem · commutative algebra

CauSeq.Completion.inv_mul_cancel

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α] {β : Type u_2}
  [inst_3 : DivisionRing β] {abv : β → α} [inst_4 : IsAbsoluteValue abv] {x : CauSeq.Completion.Cauchy abv},
  x ≠ 0 → x⁻¹ * x = 1

Defined in

Mathlib.Algebra.Order.CauSeq.Completion

Cited by

0 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingDivisionRingIsAbsoluteValue