Theorems · Theorem · group theory
Set.mul_subset_iff
∀ {α : Type u_2} [inst : Mul α] {s t u : Set α}, s * t ⊆ u ↔ ∀ x ∈ s, ∀ y ∈ t, x * y ∈ u- Cited by
- 6 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Set.mulstatement · cited by 297
- Set.image2_subset_iffproof · cited by 30
Cited by6
Results whose statement or proof uses this declaration.
- Submonoid.mul_subsetproof · cited by 2
- IsOpen.mul_closureproof · cited by 2
- Algebra.IsLocalIso.transproof · cited by 1
- IsTopologicalGroup.exist_mul_closure_nhdsproof · cited by 1
- MvPolynomial.restrictSupport_addproof · cited by 1
- Algebra.fg_transproof · cited by 0