Mathlib Map

Theorems · Theorem · ring theory

star_one

∀ (R : Type u) [inst : MulOneClass R] [inst_1 : StarMul R], star 1 = 1
Defined in
Mathlib.Algebra.Star.Basic
Cited by
33 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
MulOneClassStarMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

NormedSpace.star_exp · cited by 4NormedSpace.star_expHasDerivAt.star_conj · cited by 3HasDerivAt.star_conjIsSelfAdjoint.one · cited by 3IsSelfAdjoint.onealgebraMap_star_comm · cited by 3algebraMap_star_commCStarRing.norm_one · cited by 3CStarRing.norm_oneMatrix.conjTranspose_one · cited by 2Matrix.conjTranspose_oneLinearMap.toMatrix'_intrinsicStar · cited by 2LinearMap.toMatrix'_intri…Matrix.posDef_diagonal_iff · cited by 2Matrix.posDef_diagonal_iffstar_invOf · cited by 2star_invOfIsUnit.star_right_conjugate_nonneg_iff · cited by 2IsUnit.star_right_conjuga…Matrix.conjTranspose_permMatrix · cited by 1Matrix.conjTranspose_perm…Matrix.PosDef.diag_pos · cited by 1PosDef.diag_posCStarAlgebra.nnnorm_sub_mul_self_le · cited by 1CStarAlgebra.nnnorm_sub_m…Matrix.PosSemidef.diag_nonneg · cited by 1PosSemidef.diag_nonnegMatrix.IsAdjMatrix.isHermitian · cited by 1IsAdjMatrix.isHermitianStar.star · cited by 1082Star.starMulOneClass · cited by 1018MulOneClassStarMul · cited by 195StarMulMulOpposite.op_injective · cited by 37MulOpposite.op_injectivestarMulEquiv · cited by 7starMulEquivMulOpposite.op_one · cited by 2MulOpposite.op_oneMulEquiv.map_one · cited by 2MulEquiv.map_onestar_oneCITED BYCITES

Cites7

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

Cited by33

Results whose statement or proof uses this declaration.