Theorems · Theorem · functional analysis

Unitization.mem_unitsFstOne

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
  [inst_3 : IsScalarTower R A A] [inst_4 : SMulCommClass R A A] {x : (Unitization R A)ˣ},
  x ∈ Unitization.unitsFstOne R A ↔ (↑x).toProd.1 = 1

Defined in

Mathlib.Algebra.Algebra.Spectrum.Quasispectrum

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalSemiringModuleIsScalarTowerSMulCommClass