Theorems · Theorem · group theory
Submonoid.iSup_map_mulSingle_le
∀ {ι : Type u_4} {M : ι → Type u_5} [inst : (i : ι) → MulOneClass (M i)] [inst_1 : DecidableEq ι] {I : Set ι}
{S : (i : ι) → Submonoid (M i)}, ⨆ i, Submonoid.map (MonoidHom.mulSingle M i) (S i) ≤ Submonoid.pi I S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClassDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MonoidHomstatement · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- iSupstatement · cited by 2,415
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.mapstatement · cited by 190
- iSup_leproof · cited by 190
- MonoidHom.mulSinglestatement · cited by 21
- Submonoid.pistatement · cited by 17
- Submonoid.map_le_iff_le_comapproof · cited by 4
- Submonoid.le_comap_mulSingle_piproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.iSup_map_mulSingleproof · cited by 1