Theorems · Theorem · order theory
sup_le_sup_left
∀ {α : Type u} [inst : SemilatticeSup α] {a b : α}, a ≤ b → ∀ (c : α), c ⊔ a ≤ c ⊔ b- Defined in
- Mathlib.Order.Lattice
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_rflproof · cited by 1,558
- SemilatticeSupstatement and proof · cited by 785
- sup_le_supproof · cited by 48
Cited by20
Results whose statement or proof uses this declaration.
- sup_sdiff_selfproof · cited by 9
- OrdinalApprox.lfpApprox_mono_rightproof · cited by 7
- sdiff_le_sdiff_leftproof · cited by 6
- sup_inf_assoc_of_leproof · cited by 5
- Ideal.sup_iInf_eq_topproof · cited by 5
- le_of_inf_le_sup_leproof · cited by 4
- Ideal.sup_mul_eq_of_coprime_leftproof · cited by 4
- Ideal.sup_mul_eq_of_coprime_rightproof · cited by 3
- Submodule.sup_eq_sup_smul_of_le_smul_of_le_jacobsonproof · cited by 2
- Lattice.mem_ideal_sup_principalproof · cited by 2
- sup_sInf_le_iInf_supproof · cited by 1
- max_le_max_leftproof · cited by 1