Theorems · Theorem · order theory
subset_antisymm
∀ {α : Type u_1} [UsesSetNotationForOrder α] [inst : PartialOrder α] {a b : α}, a ⊆ b → b ⊆ a → a = bSet notation form of le_antisymm
- Defined in
- Mathlib.Order.RelClasses
- Cited by
- 150 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 8 definitions · uses no axioms
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.
- PartialOrderstatement and proof · cited by 6,410
- le_antisymmproof · cited by 2,068
Cited by150
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- IsClosedMap.closure_image_eq_of_continuousproof · cited by 6
- IntermediateField.adjoin_adjoin_leftproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- IsClosed.vadd_left_of_isCompactproof · cited by 5
- ContinuousOn.image_Icc_of_monotoneOnproof · cited by 5
- IsClosed.smul_left_of_isCompactproof · cited by 5
- jacobsonSpace_iff_locallyClosedproof · cited by 4
- Set.wcovBy_insertproof · cited by 4
- Matroid.closure_empty_eq_ground_iffproof · cited by 3
- ContinuousOn.image_Icc_of_antitoneOnproof · cited by 3
- ContinuousOn.image_Ioi_of_strictMonoOnproof · cited by 3