Theorems · Theorem · order theory
IsSublattice.preimage
∀ {F : Type u_2} {α : Type u_3} {β : Type u_4} [inst : Lattice α] [inst_1 : Lattice β] {s : Set α}
[inst_2 : FunLike F β α] [LatticeHomClass F β α], IsSublattice s → ∀ (f : F), IsSublattice (⇑f ⁻¹' s)- Defined in
- Mathlib.Order.SupClosed
- Cited by
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- Foundations
- Depth 8 from the axioms · uses propext
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Cites11
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
- Set.preimagestatement · cited by 4,946
- FunLikestatement and proof · cited by 2,560
- Latticestatement and proof · cited by 916
- IsSublatticestatement and proof · cited by 28
- IsSublattice.infClosedproof · cited by 15
- IsSublattice.supClosedproof · cited by 15
- LatticeHomClassstatement and proof · cited by 4
- InfClosed.preimageproof · cited by 1
- SupClosed.preimageproof · cited by 1
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