Theorems · Theorem · order theory
isSublattice_pi
∀ {ι : Type u_6} {α : ι → Type u_7} [inst : (i : ι) → Lattice (α i)] {s : Set ι} {t : (i : ι) → Set (α i)},
(∀ i ∈ s, IsSublattice (t i)) → IsSublattice (s.pi t)- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
- Assumes
- Lattice
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Cites8
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
- Latticestatement and proof · cited by 916
- Set.pistatement · cited by 405
- IsSublatticestatement and proof · cited by 28
- IsSublattice.infClosedproof · cited by 15
- IsSublattice.supClosedproof · cited by 15
- infClosed_piproof · cited by 1
- supClosed_piproof · cited by 1
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