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Theorems · Theorem · order theory

BooleanSubalgebra.closure_le

∀ {α : Type u_2} [inst : BooleanAlgebra α] {L : BooleanSubalgebra α} {s : Set α},
  BooleanSubalgebra.closure s ≤ L ↔ s ⊆ ↑L
Defined in
Mathlib.Order.BooleanSubalgebra
Cited by
2 results in Mathlib
Foundations
Depth 67 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.

BooleanSubalgebra.closure_bot_sup_induction · cited by 2BooleanSubalgebra.closure…BooleanSubalgebra.closure_latticeClosure · cited by 0BooleanSubalgebra.closure…Set · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeLE.le.trans · cited by 3151le.transBooleanAlgebra · cited by 300BooleanAlgebrasInf_le · cited by 110sInf_leBooleanSubalgebra · cited by 104BooleanSubalgebraBooleanSubalgebra.closure · cited by 12BooleanSubalgebra.closureBooleanSubalgebra.subset_closure · cited by 9BooleanSubalgebra.subset_…BooleanSubalgebra.closure_leCITED BYCITES

Cites8

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.