Theorems · Theorem · order theory
Lattice.isStronglyAtomic
∀ {α : Type u_2} [inst : Lattice α] [inst_1 : OrderBot α] [IsUpperModularLattice α] [IsAtomistic α], IsStronglyAtomic αAn upper-modular lattice that is atomistic is strongly atomic. Not an instance to prevent loops.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Bot.botproof · cited by 4,720
- LT.lt.leproof · cited by 2,189
- OrderBotstatement and proof · cited by 1,055
- Latticestatement and proof · cited by 916
- LT.lt.not_geproof · cited by 305
- CovByproof · cited by 290
- IsLUBproof · cited by 280
- sup_leproof · cited by 159
- IsAtomproof · cited by 130
- by_contraproof · cited by 60
- inf_eq_leftproof · cited by 41
Cited by1
Results whose statement or proof uses this declaration.
- Lattice.isStronglyCoatomicproof · cited by 0