Theorems · Theorem · group theory
Submonoid.closure_prod
∀ {N : Type u_2} [inst : MulOneClass N] {M : Type u_5} [inst_1 : MulOneClass M] {s : Set M} {t : Set N},
1 ∈ s → 1 ∈ t → Submonoid.closure (s ×ˢ t) = (Submonoid.closure s).prod (Submonoid.closure t)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClassMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Submonoidstatement · cited by 3,086
- le_antisymmproof · cited by 2,068
- SProd.sprodstatement · cited by 1,750
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.closurestatement and proof · cited by 167
- Submonoid.subset_closureproof · cited by 46
- MonoidHom.inlproof · cited by 32
- MonoidHom.inrproof · cited by 32
- Submonoid.prodstatement · cited by 27
- Submonoid.closure_leproof · cited by 27
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