Theorems · Theorem · order theory
BooleanSubalgebra.compl_mem
∀ {α : Type u_2} [inst : BooleanAlgebra α] {L : BooleanSubalgebra α} {a : α}, a ∈ L → aᶜ ∈ L- Defined in
- Mathlib.Order.BooleanSubalgebra
- Cited by
- 6 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Compl.complstatement · cited by 2,925
- BooleanAlgebrastatement and proof · cited by 300
- BooleanSubalgebrastatement and proof · cited by 104
- BooleanSubalgebra.compl_mem'proof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- BooleanSubalgebra.sdiff_memproof · cited by 5
- BooleanSubalgebra.top_memproof · cited by 5
- BooleanSubalgebra.closure_bot_sup_inductionstatement and proof · cited by 2
- BooleanSubalgebra.himp_memproof · cited by 2
- BooleanSubalgebra.compl_mem_iffproof · cited by 1
- BooleanSubalgebra.compl_mkstatement · cited by 0