Theorems · Theorem · order theory
sup_le_iff
∀ {α : Type u} [inst : SemilatticeSup α] {a b c : α}, a ⊔ b ≤ c ↔ a ≤ c ∧ b ≤ c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 58 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_transproof · cited by 985
- SemilatticeSupstatement and proof · cited by 785
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
Cited by58
Results whose statement or proof uses this declaration.
- OrderIso.map_supproof · cited by 37
- max_le_iffproof · cited by 25
- sup_sdiff_distribproof · cited by 5
- abs_le'proof · cited by 4
- sdiff_inf_distribproof · cited by 4
- Set.Ici_inter_Iciproof · cited by 4
- sup_eq_bot_iffproof · cited by 3
- mabs_le'proof · cited by 3
- sup_himp_distribproof · cited by 3
- partialSups_le_iffproof · cited by 3
- Ideal.sup_eq_prod_inf_factorsproof · cited by 3
- Equiv.Perm.OnCycleFactors.kerParam_range_eqproof · cited by 3