Theorems · Theorem · order theory
le_sup_left
∀ {α : Type u} [inst : SemilatticeSup α] {a b : α}, a ≤ a ⊔ b- Defined in
- Mathlib.Order.Lattice
- Cited by
- 265 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 12 definitions · uses no axioms
- 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
- SemilatticeSup.le_sup_leftproof · cited by 1
Cited by267
Results whose statement or proof uses this declaration.
- le_abs_selfproof · cited by 113
- measurable_fstproof · cited by 79
- Submodule.mem_supproof · cited by 73
- sup_le_iffproof · cited by 58
- sdiff_leproof · cited by 36
- le_sup_of_le_leftproof · cited by 26
- Ideal.radical_eq_sInfproof · cited by 21
- Set.left_mem_uIccproof · cited by 17
- codisjoint_iff_le_supproof · cited by 15
- inf_le_supproof · cited by 14
- Submodule.mem_sup_leftproof · cited by 14
- MeasureTheory.lintegral_add_measureproof · cited by 13
Showing the 200 most cited of 267.