Theorems · Theorem · group theory
Submonoid.le_pi_iff
∀ {ι : Type u_4} {M : ι → Type u_5} [inst : (i : ι) → MulOneClass (M i)] {I : Set ι} {S : (i : ι) → Submonoid (M i)}
{J : Submonoid ((i : ι) → M i)}, J ≤ Submonoid.pi I S ↔ ∀ i ∈ I, J ≤ Submonoid.comap (Pi.evalMonoidHom M i) (S i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClass
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Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.comapstatement · cited by 179
- Submonoid.pistatement · cited by 17
- Pi.evalMonoidHomstatement · cited by 14
- Set.subset_pi_iffproof · cited by 4
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