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Theorems · Theorem · ring theory

Unitary.mul_star_self

∀ {R : Type u_1} [inst : Monoid R] [inst_1 : StarMul R] (U : ↥(unitary R)), U * star U = 1
Defined in
Mathlib.Algebra.Star.Unitary
Cited by
3 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
MonoidStarMul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.IsHermitian.spectral_theorem · cited by 10IsHermitian.spectral_theo…Unitary.commute_self_star · cited by 0Unitary.commute_self_starUnitary.commute_star_self · cited by 0Unitary.commute_star_selfMonoid · cited by 3887MonoidSubmonoid · cited by 3086SubmonoidStar.star · cited by 1082Star.starunitary · cited by 207unitaryStarMul · cited by 195StarMulUnitary.coe_mul_star_self · cited by 2Unitary.coe_mul_star_selfUnitary.mul_star_selfCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.