Theorems · Theorem · group theory
Submonoid.prod_eq_bot_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
- 1 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement and proof · cited by 4,720
- MonoidHomproof · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- FunLikeproof · cited by 2,560
- MulOneClassstatement and proof · cited by 1,018
- MonoidHomClassproof · cited by 244
- MonoidHom.inlproof · cited by 32
- MonoidHom.inrproof · cited by 32
- Submonoid.prodstatement · cited by 27
- GaloisConnection.le_iff_leproof · cited by 17
- Submonoid.gc_map_comapproof · cited by 16
- MonoidHom.mker_inlproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.prod_eq_bot_iffproof · cited by 0