Theorems · Theorem · order theory
sup_eq_right
∀ {α : Type u} [inst : SemilatticeSup α] {a b : α}, a ⊔ b = b ↔ a ≤ b- Defined in
- Mathlib.Order.Lattice
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 7 from the axioms · 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
- le_antisymm_iffproof · cited by 62
Cited by53
Results whose statement or proof uses this declaration.
- sup_of_le_rightproof · cited by 143
- Set.uIcc_of_leproof · cited by 54
- abs_of_nonposproof · cited by 53
- Set.union_eq_rightproof · cited by 14
- Finset.exists_mem_eq_sup'proof · cited by 9
- mabs_of_le_oneproof · cited by 6
- max_eq_right_iffproof · cited by 5
- Set.uIoo_of_leproof · cited by 5
- Finset.union_eq_rightproof · cited by 5
- Submodule.CoFG.of_leproof · cited by 4
- sup_indproof · cited by 4
- IsNilpotent.isUnit_quotient_mk_iffproof · cited by 3