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Theorems · Theorem · order theory

BooleanSubalgebra.himp_mem

∀ {α : Type u_2} [inst : BooleanAlgebra α] {L : BooleanSubalgebra α} {a b : α}, a ∈ L → b ∈ L → a ⇨ b ∈ L
Defined in
Mathlib.Order.BooleanSubalgebra
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
BooleanAlgebra
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Around this declaration

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

Topology.IsConstructible.himp · cited by 0IsConstructible.himpBooleanSubalgebra.mk_himp_mk · cited by 0BooleanSubalgebra.mk_himp…Compl.compl · cited by 2925Compl.complBooleanAlgebra · cited by 300BooleanAlgebraHImp.himp · cited by 153HImp.himpBooleanSubalgebra · cited by 104BooleanSubalgebrahimp_eq · cited by 11himp_eqBooleanSubalgebra.supClosed · cited by 7BooleanSubalgebra.supClos…BooleanSubalgebra.compl_mem · cited by 6BooleanSubalgebra.compl_m…BooleanSubalgebra.himp_memCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.