Theorems · Theorem · order theory
isLUB_atoms_le
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : OrderBot α] [IsAtomistic α] (b : α), IsLUB {a | IsAtom a ∧ a ≤ b} b- Defined in
- Mathlib.Order.Atoms
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredstatement and proof · cited by 6,101
- OrderBotstatement and proof · cited by 1,055
- IsLUBstatement and proof · cited by 280
- upperBoundsproof · cited by 263
- IsAtomstatement and proof · cited by 130
- IsAtomisticstatement and proof · cited by 18
- IsAtomistic.isLUB_atomsproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- sSup_atoms_le_eqproof · cited by 1
- le_iff_atom_le_impproof · cited by 1
- isLUB_atoms_topproof · cited by 1