Theorems · Theorem · group theory
Submonoid.iSup_map_mulSingle
∀ {ι : Type u_3} [Finite ι] {M : ι → Type u_4} [inst : (i : ι) → Monoid (M i)] {P : (i : ι) → Submonoid (M i)}
[inst_1 : DecidableEq ι], ⨆ i, Submonoid.map (MonoidHom.mulSingle M i) (P i) = Submonoid.pi Set.univ P- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FiniteMonoidDecidableEq
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.
- SetLike.coeproof · cited by 8,199
- Fintypeproof · cited by 7,736
- Set.univstatement and proof · cited by 3,945
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement · cited by 3,629
- Finset.univproof · cited by 3,473
- Submonoidstatement and proof · cited by 3,086
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
- LE.le.antisymmproof · cited by 507
- Fintype.ofFiniteproof · cited by 255
- Submonoid.mapstatement and proof · cited by 190
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.FG.piproof · cited by 1