Theorems · Theorem · order theory
Set.pi_mono
∀ {ι : Type u_1} {α : ι → Type u_2} {s : Set ι} {t₁ t₂ : (i : ι) → Set (α i)},
(∀ i ∈ s, t₁ i ⊆ t₂ i) → s.pi t₁ ⊆ s.pi t₂- Defined in
- Mathlib.Data.Set.Prod
- Cited by
- 8 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
- Set.pistatement · cited by 405
- Set.Subset.rflproof · cited by 255
- Set.pi_mono'proof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- isOpen_pi_iffproof · cited by 6
- Set.pi_subset_pi_iffproof · cited by 4
- Real.volume_pi_le_prod_diamproof · cited by 1
- Filter.hasBasis_pi_same_indexproof · cited by 1
- convexHull_piproof · cited by 0
- Submodule.pi_monoproof · cited by 0
- isOpen_pi_iff'proof · cited by 0
- Subalgebra.pi_monoproof · cited by 0