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Theorems · Theorem · group theory

ZeroMemClass.coe_eq_zero

∀ {A : Type u_3} {M₁ : Type u_4} [inst : SetLike A M₁] [inst_1 : Zero M₁] [hA : ZeroMemClass A M₁] {S' : A} {x : ↥S'},
  ↑x = 0 ↔ x = 0
Defined in
Mathlib.Algebra.Group.Submonoid.Defs
Cited by
11 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
SetLikeZeroZeroMemClass
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Around this declaration

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

Subalgebra.coe_eq_zero · cited by 4Subalgebra.coe_eq_zeroModule.End.isNilpotent_restrict_genEigenspace_nat · cited by 4End.isNilpotent_restrict_…LieModule.isNilpotent_toEnd_sub_algebraMap · cited by 2LieModule.isNilpotent_toE…Submodule.LinearDisjoint.not_linearIndependent_pair_of_commute_of_flat_right · cited by 2LinearDisjoint.not_linear…Submodule.LinearDisjoint.not_linearIndependent_pair_of_commute_of_flat_left · cited by 2LinearDisjoint.not_linear…AddSubmonoid.nsmul_exponent_eq_zero · cited by 1AddSubmonoid.nsmul_expone…AddSubmonoid.isOfFinAddOrder_coe · cited by 1AddSubmonoid.isOfFinAddOr…Valuation.leIdeal_v_le_of_mem · cited by 1Valuation.leIdeal_v_le_of…NonUnitalStarSubalgebra.coe_eq_zero · cited by 0NonUnitalStarSubalgebra.c…GradedRing.mem_support_iff · cited by 0GradedRing.mem_support_iffNonUnitalSubalgebra.coe_eq_zero · cited by 0NonUnitalSubalgebra.coe_e…SetLike · cited by 1084SetLikeZeroMemClass · cited by 25ZeroMemClassZeroMemClass.coe_eq_zeroCITED BYCITES

Cites2

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Cited by11

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