Theorems · Theorem · group theory
Monoid.CoprodI.lift_mrange_le
∀ {ι : Type u_1} {M : ι → Type u_2} [inst : (i : ι) → Monoid (M i)] {N : Type u_4} [inst_1 : Monoid N]
(f : (i : ι) → M i →* N) {s : Submonoid N},
MonoidHom.mrange (Monoid.CoprodI.lift f) ≤ s ↔ ∀ (i : ι), MonoidHom.mrange (f i) ≤ s- Defined in
- Mathlib.GroupTheory.CoprodI
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equivstatement · cited by 8,337
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement and proof · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- MonoidHom.mrangestatement and proof · cited by 63
- Monoid.CoprodIstatement · cited by 52
- Monoid.CoprodI.liftstatement · cited by 21
- Monoid.CoprodI.mrange_eq_iSupproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.