Theorems · Theorem · order theory
SemilatticeSup.sup_le
∀ {α : Type u} [self : SemilatticeSup α] (a b c : α), a ≤ c → b ≤ c → SemilatticeSup.sup a b ≤ cThe supremum is the least upper bound
- Defined in
- Mathlib.Order.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeSupstatement and proof · cited by 785
- SemilatticeSup.supstatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- sup_leproof · cited by 159