Theorems · Theorem · order theory
sup_of_le_right
∀ {α : Type u} [inst : SemilatticeSup α] {a b : α}, a ≤ b → a ⊔ b = bAlias of the reverse direction of sup_eq_right.
- Defined in
- Mathlib.Order.Lattice
- Cited by
- 143 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_rightproof · cited by 53
Cited by143
Results whose statement or proof uses this declaration.
- Monotone.map_maxproof · cited by 55
- Set.uIoc_of_leproof · cited by 38
- bot_sup_eqproof · cited by 32
- intervalIntegral.integral_congrproof · cited by 18
- Set.projIcc_of_memproof · cited by 11
- Set.uIoc_eq_unionproof · cited by 8
- Unitization.norm_inrproof · cited by 8
- Monotone.map_supproof · cited by 6
- max_zero_sub_max_neg_zero_eq_selfproof · cited by 6
- sup_top_eqproof · cited by 6
- Ideal.sup_iInf_eq_topproof · cited by 5
- Antitone.map_maxproof · cited by 5