Theorems · Theorem · order theory
BooleanSubalgebra.bot_mem
∀ {α : Type u_2} [inst : BooleanAlgebra α] {L : BooleanSubalgebra α}, ⊥ ∈ 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- BooleanAlgebrastatement and proof · cited by 300
- BooleanSubalgebrastatement and proof · cited by 104
- BooleanSubalgebra.bot_mem'proof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- BooleanSubalgebra.top_memproof · cited by 5
- BooleanSubalgebra.closure_bot_sup_inductionstatement and proof · cited by 2
- BooleanSubalgebra.sSup_memproof · cited by 1
- Topology.IsConstructible.emptyproof · cited by 1
- BooleanSubalgebra.biSup_memproof · cited by 1
- BooleanSubalgebra.iSup_memproof · cited by 1
- BooleanSubalgebra.mk_botstatement · cited by 0