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Theorems · Theorem · ring theory

star_star

∀ {R : Type u} [inst : InvolutiveStar R] (r : R), star (star r) = r
Defined in
Mathlib.Algebra.Star.Basic
Cited by
135 results in Mathlib
Foundations
Depth 3 from the axioms, rests on 6 definitions · uses no axioms
Assumes
InvolutiveStar
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Around this declaration

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

Matrix.conjTranspose_conjTranspose · cited by 31Matrix.conjTranspose_conj…norm_star · cited by 16norm_starIsSelfAdjoint.star_mul_self · cited by 12IsSelfAdjoint.star_mul_se…CStarAlgebra.isStrictlyPositive_TFAE · cited by 7CStarAlgebra.isStrictlyPo…CStarAlgebra.nonneg_TFAE · cited by 6CStarAlgebra.nonneg_TFAEstar_le_star_iff · cited by 6star_le_star_iffmul_star_self_nonneg · cited by 5mul_star_self_nonnegcfcₙ_star · cited by 4cfcₙ_starStarAlgebra.gc · cited by 4StarAlgebra.gcCStarRing.norm_self_mul_star · cited by 4CStarRing.norm_self_mul_s…starRingEnd_self_apply · cited by 3starRingEnd_self_applycfc_star · cited by 3cfc_starMatrix.posSemidef_conjTranspose_mul_self · cited by 3Matrix.posSemidef_conjTra…NumberField.ComplexEmbedding.involutive_conjugate · cited by 3ComplexEmbedding.involuti…NonUnitalStarAlgebra.gc · cited by 3NonUnitalStarAlgebra.gcStar.star · cited by 1082Star.starInvolutiveStar · cited by 52InvolutiveStarInvolutiveStar.star_involutive · cited by 11InvolutiveStar.star_invol…star_starCITED BYCITES

Cites3

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

Cited by135

Results whose statement or proof uses this declaration.