Theorems · Theorem · order theory
Lattice.isStronglyCoatomic
∀ {α : Type u_2} [inst : Lattice α] [inst_1 : OrderTop α] [IsLowerModularLattice α] [IsCoatomistic α],
IsStronglyCoatomic αA lower-modular lattice that is coatomistic is strongly coatomic. Not an instance to prevent loops.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Latticestatement and proof · cited by 916
- OrderTopstatement and proof · cited by 493
- IsStronglyCoatomicstatement · cited by 12
- IsCoatomisticstatement and proof · cited by 7
- IsLowerModularLatticestatement and proof · cited by 6
- isStronglyAtomic_dual_iff_is_stronglyCoatomicproof · cited by 5
- Lattice.isStronglyAtomicproof · cited by 1
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