Theorems · Theorem · group theory
AddMonoid.Coprod.mclosure_range_inl_union_inr
∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N],
AddSubmonoid.closure (Set.range ⇑AddMonoid.Coprod.inl ∪ Set.range ⇑AddMonoid.Coprod.inr) = ⊤- Defined in
- Mathlib.GroupTheory.Coprod.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Top.topstatement · cited by 9,680
- Set.rangestatement and proof · cited by 4,705
- AddMonoidHomstatement · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- Set.range_compproof · cited by 223
- FreeAddMonoidproof · cited by 145
- AddMonoid.Coprodstatement and proof · cited by 104
- AddSubmonoid.mapproof · cited by 99
Cited by3
Results whose statement or proof uses this declaration.
- AddMonoid.Coprod.hom_extproof · cited by 12
- AddMonoid.Coprod.mrange_inl_sup_mrange_inrproof · cited by 2
- AddMonoid.Coprod.closure_range_inl_union_inrproof · cited by 1