Theorems · Theorem · group theory
Set.smul_set_mono
∀ {α : Type u_2} {β : Type u_3} [inst : SMul α β] {s t : Set β} {a : α}, s ⊆ t → a • s ⊆ a • t- Cited by
- 15 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SMul
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.smulSetstatement · cited by 608
- Set.image_monoproof · cited by 197
Cited by15
Results whose statement or proof uses this declaration.
- Balanced.smul_monoproof · cited by 6
- Absorbs.mono_leftproof · cited by 5
- gauge_monoproof · cited by 4
- GroupFilterBasis.nhds_eqproof · cited by 3
- FiniteDimensional.of_totallyBounded_nhds_zeroproof · cited by 3
- LinearMap.isBigOTVS_rev_compproof · cited by 2
- Balanced.smulproof · cited by 1
- MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_oneproof · cited by 1
- NormedSpace.isBounded_iff_subset_smul_closedBallproof · cited by 1
- FreeGroup.injective_lift_of_ping_pongproof · cited by 0