Theorems · Theorem · order theory
sup_of_le_left
∀ {α : Type u} [inst : SemilatticeSup α] {a b : α}, b ≤ a → a ⊔ b = aAlias of the reverse direction of sup_eq_left.
- Defined in
- Mathlib.Order.Lattice
- Cited by
- 218 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 24 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.
- SemilatticeSupstatement and proof · cited by 785
- sup_eq_leftproof · cited by 71
Cited by218
Results whose statement or proof uses this declaration.
- Monotone.map_maxproof · cited by 55
- sup_bot_eqproof · cited by 31
- sup_idemproof · cited by 29
- intervalIntegral.integral_congrproof · cited by 18
- Real.enorm_of_nonnegproof · cited by 10
- top_sup_eqproof · cited by 8
- Set.uIoc_eq_unionproof · cited by 8
- sdiff_supproof · cited by 7
- Set.uIoc_of_geproof · cited by 6
- AnalyticAt.zpow_nonnegproof · cited by 6
- Real.toNNReal_mulproof · cited by 6
- Monotone.map_supproof · cited by 6
Showing the 200 most cited of 218.