Theorems · Theorem · group theory
AddSubmonoid.closure_zero_prod
∀ {N : Type u_2} [inst : AddZeroClass N] {M : Type u_5} [inst_1 : AddZeroClass M] (t : Set N),
AddSubmonoid.closure ({0} ×ˢ t) = ⊥.prod (AddSubmonoid.closure t)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Bot.botstatement · cited by 4,720
- le_antisymmproof · cited by 2,068
- SProd.sprodstatement and proof · cited by 1,750
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- bot_leproof · cited by 306
- Set.Subset.rflproof · cited by 255
- AddSubmonoid.closurestatement and proof · cited by 224
- AddSubmonoid.subset_closureproof · cited by 63
- AddSubmonoid.closure_leproof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.FG.prodproof · cited by 1