Theorems · Theorem · order theory
Set.prod_mono_left
∀ {α : Type u_1} {β : Type u_2} {s₁ s₂ : Set α} {t : Set β}, s₁ ⊆ s₂ → s₁ ×ˢ t ⊆ s₂ ×ˢ t- Defined in
- Mathlib.Data.Set.Prod
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- SProd.sprodstatement · cited by 1,750
- Set.Subset.rflproof · cited by 255
- Set.prod_monoproof · cited by 52
Cited by7
Results whose statement or proof uses this declaration.
- ContMDiffWithinAt.mfderivWithinproof · cited by 3
- prod_nhdsSet_le_of_disjoint_cocompactproof · cited by 1
- Set.prod_subset_prod_leftproof · cited by 1
- generalized_tube_lemma_rightproof · cited by 0
- Ideal.prod_mono_leftproof · cited by 0
- UpperSet.prod_mono_leftproof · cited by 0
- LowerSet.prod_mono_leftproof · cited by 0