Theorems · Theorem · group theory
AddSubmonoid.prod_eq_top_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
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClassAddZeroClass
Around this declaration
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Cites11
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
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- eq_top_iffproof · cited by 236
- AddMonoidHom.sndproof · cited by 42
- AddMonoidHom.fstproof · cited by 39
- AddSubmonoid.prodstatement · cited by 27
- AddMonoidHom.mrange_eq_mapproof · cited by 15
- AddSubmonoid.le_prod_iffproof · cited by 2
- AddSubmonoid.mrange_fstproof · cited by 1
- AddSubmonoid.mrange_sndproof · cited by 1
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