Theorems · Theorem · order theory
LE.le.ge_iff_eq
∀ {α : Type u_2} [inst : PartialOrder α] {a b : α}, a ≤ b → (b ≤ a ↔ a = b)- Defined in
- Mathlib.Order.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 7 from the axioms · 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.le.antisymmproof · cited by 507
- Eq.geproof · cited by 375
Cited by12
Results whose statement or proof uses this declaration.
- top_le_iffproof · cited by 175
- Finset.card_filter_eq_iffproof · cited by 2
- InnerProductGeometry.angle_eq_angle_add_add_angle_addproof · cited by 2
- inf_eq_supproof · cited by 2
- Polynomial.Monic.eq_X_pow_iff_natTrailingDegree_eq_natDegreeproof · cited by 1
- WeierstrassCurve.hasGoodReduction_iff_isElliptic_reductionproof · cited by 1
- Real.geom_mean_lt_arith_mean_weighted_iff_of_pos'proof · cited by 1
- SimpleGraph.chromaticNumber_eq_card_iff_forall_surjectiveproof · cited by 1
- SimpleGraph.chromaticNumber_eq_iff_forall_surjectiveproof · cited by 1
- AddSubgroup.isSimpleAddGroup_iffproof · cited by 0
- Set.Ici_eq_singleton_iff_isTopproof · cited by 0