Theorems · Theorem · order theory
sup_eq_left
∀ {α : Type u} [inst : SemilatticeSup α] {a b : α}, a ⊔ b = a ↔ b ≤ a- Defined in
- Mathlib.Order.Lattice
- Cited by
- 71 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- 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
- le_antisymm_iffproof · cited by 62
Cited by71
Results whose statement or proof uses this declaration.
- abs_of_nonnegproof · cited by 279
- sup_of_le_leftproof · cited by 218
- Set.uIcc_of_geproof · cited by 22
- mabs_of_one_leproof · cited by 11
- Finset.exists_mem_eq_sup'proof · cited by 9
- Submodule.le_of_le_smul_of_le_jacobson_botproof · cited by 9
- Ideal.comap_isMaximal_of_surjectiveproof · cited by 8
- posPart_eq_selfproof · cited by 6
- Set.union_eq_leftproof · cited by 6
- left_eq_supproof · cited by 5
- max_eq_left_iffproof · cited by 4
- sup_indproof · cited by 4