Theorems · Theorem · group theory
AddSubmonoid.prod_bot_sup_bot_prod
∀ {N : Type u_2} [inst : AddZeroClass N] {M : Type u_5} [inst_1 : AddZeroClass M] (s : AddSubmonoid M)
(t : AddSubmonoid N), s.prod ⊥ ⊔ ⊥.prod t = s.prod t- Cited by
- 2 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- bot_leproof · cited by 306
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- AddMemClass.add_memproof · cited by 229
- Set.mem_singletonproof · cited by 183
- sup_leproof · cited by 159
- AddSubmonoid.prodstatement and proof · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.mrange_inl_sup_mrange_inrproof · cited by 1
- AddSubmonoid.FG.prodproof · cited by 1