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Theorems · Theorem · group theory

Set.center_prod

∀ {M : Type u_1} [inst : Mul M] {N : Type u_2} [inst_1 : Mul N], Set.center (M × N) = Set.center M ×ˢ Set.center N
Defined in
Mathlib.Algebra.Group.Center
Cited by
10 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
MulMul
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Around this declaration

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

NonUnitalSubalgebra.center_prod · cited by 0NonUnitalSubalgebra.cente…Subalgebra.center_prod · cited by 0Subalgebra.center_prodSubsemigroup.center_prod · cited by 0Subsemigroup.center_prodNonUnitalSubring.center_prod · cited by 0NonUnitalSubring.center_p…Subring.center_prod · cited by 0Subring.center_prodSubmonoid.center_prod · cited by 0Submonoid.center_prodSubsemiring.center_prod · cited by 0Subsemiring.center_prodSubgroup.center_prod · cited by 0Subgroup.center_prodNonUnitalStarSubalgebra.center_prod · cited by 0NonUnitalStarSubalgebra.c…NonUnitalSubsemiring.center_prod · cited by 0NonUnitalSubsemiring.cent…Set · cited by 53352SetSet.ext · cited by 2266Set.extSProd.sprod · cited by 1750SProd.sprodSet.center · cited by 49Set.centerSet.center_prodCITED BYCITES

Cites4

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

Cited by10

Results whose statement or proof uses this declaration.