Mathlib Map

Theorems · Definition · group theory

Submonoid.prod

{N : Type u_2} →
  [inst : MulOneClass N] → {M : Type u_5} → [inst_1 : MulOneClass M] → Submonoid M → Submonoid N → Submonoid (M × N)

Given Submonoids s, t of Monoids M, N respectively, s × t as a Submonoid of M × N.

Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
27 results in Mathlib
Foundations
Depth 14 from the axioms · uses no axioms
Assumes
MulOneClassMulOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Subgroup.prod · cited by 35Subgroup.prodSubring.prod · cited by 11Subring.prodSubsemiring.prod · cited by 11Subsemiring.prodSubmonoid.prod_le_iff · cited by 4Submonoid.prod_le_iffSubmonoid.top_prod · cited by 2Submonoid.top_prodSubmonoid.prod_bot_sup_bot_prod · cited by 2Submonoid.prod_bot_sup_bo…Submonoid.mrange_inl · cited by 2Submonoid.mrange_inlSubmonoid.mrange_inr · cited by 2Submonoid.mrange_inrSubmonoid.closure_one_prod · cited by 1Submonoid.closure_one_prodSubmonoid.map_inl · cited by 1Submonoid.map_inlSubmonoid.map_inr · cited by 1Submonoid.map_inrSubmonoid.closure_prod_one · cited by 1Submonoid.closure_prod_oneSubmonoid.top_prod_top · cited by 1Submonoid.top_prod_topSubmonoid.FG.prod · cited by 1FG.prodSubmonoid.prod_eq_bot_iff · cited by 1Submonoid.prod_eq_bot_iffSetLike.coe · cited by 8199SetLike.coeSubmonoid · cited by 3086SubmonoidSProd.sprod · cited by 1750SProd.sprodMulOneClass · cited by 1018MulOneClassSubmonoid.prodCITED BYCITES

Cites4

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

Cited by31

Results whose statement or proof uses this declaration.