Theorems · Theorem · order theory
BooleanSubalgebra.infClosed
∀ {α : Type u_2} [inst : BooleanAlgebra α] (L : BooleanSubalgebra α), InfClosed ↑L- Defined in
- Mathlib.Order.BooleanSubalgebra
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BooleanAlgebra
Around this declaration
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.
- SetLike.coestatement · cited by 8,199
- BooleanAlgebrastatement and proof · cited by 300
- BooleanSubalgebrastatement and proof · cited by 104
- InfClosedstatement · cited by 57
- BooleanSubalgebra.toSublatticeproof · cited by 7
- Sublattice.infClosed'proof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- BooleanSubalgebra.sdiff_memproof · cited by 5
- BooleanSubalgebra.closure_bot_sup_inductionproof · cited by 2
- BooleanSubalgebra.iInf_memproof · cited by 1
- BooleanSubalgebra.sInf_memproof · cited by 1
- BooleanSubalgebra.biInf_memproof · cited by 1
- BooleanSubalgebra.inf_memproof · cited by 1
- BooleanSubalgebra.mk_inf_mkstatement · cited by 0