Theorems · Theorem · group theory
Submonoid.prod_eq_top_iff
∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] {s : Submonoid M} {t : Submonoid N},
s.prod t = ⊤ ↔ s = ⊤ ∧ t = ⊤- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Submonoidstatement and proof · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- MonoidHom.sndproof · cited by 31
- MonoidHom.fstproof · cited by 28
- Submonoid.prodstatement · cited by 27
- Submonoid.mrange_fstproof · cited by 1
- Submonoid.mrange_sndproof · cited by 1
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