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Theorems · Theorem · group theory

IsMulCentral.left_assoc

∀ {M : Type u_1} [inst : Mul M] {z : M}, IsMulCentral z → ∀ (b c : M), z * (b * c) = z * b * c

associative property for left multiplication

Defined in
Mathlib.Algebra.Group.Center
Cited by
7 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
Mul
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Around this declaration

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

IsMulCentral.mid_assoc · cited by 1IsMulCentral.mid_assocSet.intCast_mem_center · cited by 0Set.intCast_mem_centerSet.neg_mem_center · cited by 0Set.neg_mem_centerSet.smul_mem_center · cited by 0Set.smul_mem_centerSet.add_mem_center · cited by 0Set.add_mem_centerModule.Basis.mem_center_iff · cited by 0Basis.mem_center_iffSet.star_mem_center · cited by 0Set.star_mem_centerIsMulCentral · cited by 13IsMulCentralIsMulCentral.left_assocCITED BYCITES

Cites1

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

Cited by7

Results whose statement or proof uses this declaration.