Theorems · Theorem · order theory
sup_congr_left
∀ {α : Type u} [inst : SemilatticeSup α] {a b c : α}, b ≤ a ⊔ c → c ≤ a ⊔ b → a ⊔ b = a ⊔ c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeSupstatement and proof · cited by 785
- LE.le.antisymmproof · cited by 507
- le_sup_leftproof · cited by 265
- sup_leproof · cited by 159
Cited by4
Results whose statement or proof uses this declaration.
- sup_sdiff_eq_supproof · cited by 3
- sup_eq_sup_iff_leftproof · cited by 2
- Set.union_congr_leftproof · cited by 0
- Finset.union_congr_leftproof · cited by 0