Theorems · Theorem · order theory
BooleanAlgebra.le_iff_atom_le_imp
∀ {α : Type u_4} [inst : BooleanAlgebra α] [IsAtomic α] {x y : α}, x ≤ y ↔ ∀ (a : α), IsAtom a → a ≤ x → a ≤ y- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BooleanAlgebraIsAtomic
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- Compl.complproof · cited by 2,925
- le_transproof · cited by 985
- BooleanAlgebrastatement and proof · cited by 300
- compl_complproof · cited by 229
- IsAtomstatement and proof · cited by 130
- of_not_notproof · cited by 51
- le_inf_iffproof · cited by 48
- IsAtomicstatement and proof · cited by 20
- IsAtomic.eq_bot_or_exists_atom_leproof · cited by 12
- eq_compl_iff_isComplproof · cited by 6
- inf_compl_selfproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- BooleanAlgebra.eq_iff_atom_le_iffproof · cited by 0