Theorems · Theorem · order theory
IsSublattice.dual
∀ {α : Type u_3} [inst : Lattice α] {s : Set α}, IsSublattice s → IsSublattice (⇑OrderDual.ofDual ⁻¹' s)Alias of the reverse direction of isSublattice_preimage_ofDual.
- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses Quot.sound
- Assumes
- Lattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.preimagestatement · cited by 4,946
- OrderDualstatement · cited by 927
- Latticestatement and proof · cited by 916
- OrderDual.ofDualstatement · cited by 400
- IsSublatticestatement · cited by 28
- isSublattice_preimage_ofDualproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.