Theorems · Theorem · order theory
IsModularLattice.exists_disjoint_and_sup_eq
∀ {α : Type u_1} [inst : Lattice α] [IsModularLattice α] {a b : α} [inst_2 : BoundedOrder α] [ComplementedLattice α],
a ≤ b → ∃ a', Disjoint a a' ∧ a ⊔ a' = b- Defined in
- Mathlib.Order.ModularLattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Disjointstatement · cited by 2,201
- Latticestatement and proof · cited by 916
- BoundedOrderstatement and proof · cited by 270
- IsModularLatticestatement and proof · cited by 86
- ComplementedLatticestatement and proof · cited by 30
- IsModularLattice.exists_inf_eq_and_sup_eqproof · cited by 2
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