Theorems · Theorem · group theory
AddSubmonoid.prod_eq_bot_iff
∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {s : AddSubmonoid M}
{t : AddSubmonoid 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
- AddZeroClassAddZeroClass
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.
- Bot.botstatement and proof · cited by 4,720
- AddMonoidHomproof · cited by 3,230
- FunLikeproof · cited by 2,560
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddMonoidHomClassproof · cited by 252
- eq_bot_iffproof · cited by 159
- AddMonoidHom.inlproof · cited by 29
- AddMonoidHom.inrproof · cited by 29
- AddSubmonoid.prodstatement · cited by 27
- GaloisConnection.le_iff_leproof · cited by 17
- AddSubmonoid.gc_map_comapproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.prod_eq_bot_iffproof · cited by 1