Mathlib Map

Theorems · Theorem · ring theory

star_zero

∀ (R : Type u) [inst : AddMonoid R] [inst_1 : StarAddMonoid R], star 0 = 0
Defined in
Mathlib.Algebra.Star.Basic
Cited by
58 results in Mathlib
Foundations
Depth 19 from the axioms · uses Quot.sound
Assumes
AddMonoidStarAddMonoid
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Around this declaration

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

Matrix.posSemidef_iff_dotProduct_mulVec · cited by 5Matrix.posSemidef_iff_dot…cfcₙ_re_id · cited by 4cfcₙ_re_idcfcₙ_star · cited by 4cfcₙ_starCFC.abs_eq_cfcₙ_coe_norm · cited by 4CFC.abs_eq_cfcₙ_coe_normMatrix.conjTranspose_natCast · cited by 3Matrix.conjTranspose_natC…Unitization.inr_star · cited by 3Unitization.inr_starMatrix.posDef_iff_dotProduct_mulVec · cited by 3Matrix.posDef_iff_dotProd…cfc_star · cited by 3cfc_starIsSelfAdjoint.zero · cited by 3IsSelfAdjoint.zeroMatrix.PosSemidef.submatrix · cited by 3PosSemidef.submatrixisSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts · cited by 2isSelfAdjoint_iff_isStarN…Matrix.conjTranspose_one · cited by 2Matrix.conjTranspose_oneQuaternion.sq_eq_neg_normSq · cited by 2Quaternion.sq_eq_neg_norm…QuadraticAlgebra.star_mem_nonZeroDivisors · cited by 2QuadraticAlgebra.star_mem…Ring.inverse_star · cited by 2Ring.inverse_starAddMonoid · cited by 2864AddMonoidStar.star · cited by 1082Star.starStarAddMonoid · cited by 296StarAddMonoidstarAddEquiv · cited by 25starAddEquivAddEquiv.map_zero · cited by 9AddEquiv.map_zerostar_zeroCITED BYCITES

Cites5

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

Cited by58

Results whose statement or proof uses this declaration.