Theorems · Theorem · group theory
AddSubmonoid.closure_eq_mrange
∀ {M : Type u_1} [inst : AddMonoid M] (s : Set M),
AddSubmonoid.closure s = AddMonoidHom.mrange (FreeAddMonoid.lift Subtype.val)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- AddMonoidHomstatement · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- FreeAddMonoidstatement · cited by 145
- Subtype.range_coeproof · cited by 98
- AddMonoidHom.mrangestatement · cited by 61
- FreeAddMonoid.liftstatement · cited by 24
- FreeAddMonoid.mrange_liftproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- AddSubmonoid.closure_induction_leftproof · cited by 3
- AddSubmonoid.closure_eq_image_sumproof · cited by 2
- AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjectiveproof · cited by 1