Theorems · Theorem · order theory
sup_comm
∀ {α : Type u} [inst : SemilatticeSup α] (a b : α), a ⊔ b = b ⊔ a- Defined in
- Mathlib.Order.Lattice
- Cited by
- 165 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 19 definitions · 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.
- le_antisymmproof · cited by 2,068
- SemilatticeSupstatement and proof · cited by 785
Cited by166
Results whose statement or proof uses this declaration.
- abs_nonnegproof · cited by 168
- abs_negproof · cited by 93
- inf_sup_leftproof · cited by 28
- Finset.union_commproof · cited by 25
- symmDiff_commproof · cited by 23
- sup_inf_rightproof · cited by 22
- sdiff_le_iff'proof · cited by 20
- Set.uIcc_commproof · cited by 18
- mabs_invproof · cited by 13
- iSup_bool_eqproof · cited by 12
- Metric.hausdorffEDist_commproof · cited by 11
- one_le_mabsproof · cited by 11