Theorems · Theorem · order theory
eq_of_forall_ge_iff
∀ {α : Type u_2} [inst : PartialOrder α] {a b : α}, (∀ (c : α), a ≤ c ↔ b ≤ c) → a = b- Defined in
- Mathlib.Order.Basic
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- PartialOrder
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.
- PartialOrderstatement and proof · cited by 6,410
- le_rflproof · cited by 1,558
- LE.le.antisymm'proof · cited by 104
Cited by96
Results whose statement or proof uses this declaration.
- Finset.sup'_congrproof · cited by 38
- sup_assocproof · cited by 37
- OrderIso.map_iSupproof · cited by 25
- sdiff_botproof · cited by 13
- Isometry.ediam_imageproof · cited by 12
- Algebra.adjoin_imageproof · cited by 11
- Int.ceil_intCastproof · cited by 11
- Subgroup.zpowers_invproof · cited by 11
- iSup_prodproof · cited by 10
- Ordinal.one_opowproof · cited by 9
- Ordinal.opow_addproof · cited by 9
- Finset.sup_unionproof · cited by 9