Theorems · Definition · order theory

BooleanSubalgebra.comap

{α : Type u_2} →
  {β : Type u_3} →
    [inst : BooleanAlgebra α] →
      [inst_1 : BooleanAlgebra β] → BoundedLatticeHom α β → BooleanSubalgebra β → BooleanSubalgebra α

The preimage of a Boolean subalgebra along a bounded lattice homomorphism.

Defined in: Mathlib.Order.BooleanSubalgebra
Cited by: 14 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: BooleanAlgebra BooleanAlgebra

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
SetLike.coeproof · cited by 8,199
Set.preimageproof · cited by 4,946
BooleanAlgebrastatement and proof · cited by 300
BoundedLatticeHomstatement and proof · cited by 185
BooleanSubalgebrastatement and proof · cited by 104

Cited by14

Results whose statement or proof uses this declaration.

BooleanSubalgebra.gc_map_comapstatement · cited by 6
BooleanSubalgebra.comap_monostatement · cited by 2
BooleanSubalgebra.map_equiv_eq_comap_symmstatement and proof · cited by 1
BooleanSubalgebra.map_le_iff_le_comapstatement · cited by 1
BooleanSubalgebra.comap_comapstatement · cited by 0
BooleanSubalgebra.comap_equiv_eq_map_symmstatement · cited by 0
BooleanSubalgebra.comap_iInfstatement · cited by 0
BooleanSubalgebra.comap_idstatement · cited by 0
BooleanSubalgebra.comap_infstatement · cited by 0
BooleanSubalgebra.comap_topstatement · cited by 0
BooleanSubalgebra.mem_comapstatement · cited by 0
BooleanSubalgebra.le_comap_iSupstatement · cited by 0