Theorems · Theorem · order theory
BooleanAlgebra.inf_compl_le_bot
∀ {α : Type u} [self : BooleanAlgebra α] (x : α), x ⊓ xᶜ ≤ ⊥The infimum of x and xᶜ is at most ⊥
- Defined in
- Mathlib.Order.BooleanAlgebra.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- BooleanAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- Compl.complstatement · cited by 2,925
- BooleanAlgebrastatement and proof · cited by 300
- Lattice.infstatement · cited by 18
- Lattice.inf_le_leftstatement · cited by 12
- Lattice.inf_le_rightstatement · cited by 12
- Lattice.le_infstatement · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- inf_compl_eq_bot'proof · cited by 1
- Fintype.toCompleteBooleanAlgebraproof · cited by 0
- Function.Injective.completeBooleanAlgebraproof · cited by 0
- IsSimpleOrder.completeBooleanAlgebraproof · cited by 0