Theorems · Theorem · group theory
Submonoid.mul_subset
∀ {M : Type u_3} [inst : Monoid M] {s t : Set M} {S : Submonoid M}, s ⊆ ↑S → t ⊆ ↑S → s * t ⊆ ↑S- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SetLike.coestatement and proof · cited by 8,199
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- Set.mulstatement · cited by 297
- MulMemClass.mul_memproof · cited by 173
- Set.mul_subset_iffproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.mul_subset_closureproof · cited by 0
- Subgroup.mul_subsetproof · cited by 0