Theorems · Definition · order theory
IsSimpleOrder.completeBooleanAlgebra
{α : Type u_2} → [inst : Lattice α] → [inst_1 : BoundedOrder α] → [IsSimpleOrder α] → CompleteBooleanAlgebra αA simple BoundedOrder is also a CompleteBooleanAlgebra.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteLatticeproof · cited by 1,048
- Latticestatement and proof · cited by 916
- BooleanAlgebraproof · cited by 300
- BoundedOrderstatement and proof · cited by 270
- IsSimpleOrderstatement and proof · cited by 54
- CompleteBooleanAlgebrastatement · cited by 32
- BooleanAlgebra.himp_eqproof · cited by 2
- BooleanAlgebra.sdiff_eqproof · cited by 1
- BooleanAlgebra.top_le_sup_complproof · cited by 1
- BooleanAlgebra.inf_compl_le_botproof · cited by 1
- IsSimpleOrder.completeLatticeproof · cited by 0
- IsSimpleOrder.booleanAlgebraproof · cited by 0
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