Theorems · Definition · order theory

BooleanSubalgebra.map

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

The image of a Boolean subalgebra along a monoid homomorphism is a Boolean subalgebra.

Defined in: Mathlib.Order.BooleanSubalgebra
Cited by: 20 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.imageproof · cited by 5,609
BooleanAlgebrastatement and proof · cited by 300
BoundedLatticeHomstatement and proof · cited by 185
BooleanSubalgebrastatement and proof · cited by 104

Cited by20

Results whose statement or proof uses this declaration.

BooleanSubalgebra.gc_map_comapstatement · cited by 6
BooleanSubalgebra.map_equiv_eq_comap_symmstatement and proof · cited by 1
BooleanSubalgebra.map_le_iff_le_comapstatement · cited by 1
BooleanSubalgebra.map_monostatement · cited by 1
BooleanSubalgebra.mem_map_of_memstatement · cited by 1
BooleanSubalgebra.apply_coe_mem_mapstatement · cited by 0
BooleanSubalgebra.apply_mem_map_iffstatement · cited by 0
BooleanSubalgebra.map_botstatement · cited by 0
BooleanSubalgebra.map_iSupstatement · cited by 0
BooleanSubalgebra.map_idstatement and proof · cited by 0
BooleanSubalgebra.map_infstatement · cited by 0
BooleanSubalgebra.map_inf_lestatement · cited by 0