Theorems · Theorem · order theory
subset_antisymm_iff
∀ {α : Type u_1} [UsesSetNotationForOrder α] [inst : PartialOrder α] {a b : α}, a = b ↔ a ⊆ b ∧ b ⊆ aSet notation form of le_antisymm_iff
- Defined in
- Mathlib.Order.RelClasses
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 7 from the axioms · 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_antisymm_iffproof · cited by 62
Cited by17
Results whose statement or proof uses this declaration.
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
- Matroid.Indep.closure_eq_setOfPred_isBasis_insertproof · cited by 6
- Matroid.closure_union_eq_of_subset_coloopsproof · cited by 4
- Matroid.Indep.closure_inter_eq_self_of_subsetproof · cited by 4
- Topology.IsUpperSet.closure_eq_lowerClosureproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- isClosed_preimage_valproof · cited by 2
- AddGroupFilterBasis.t2Space_iff_sInter_subsetproof · cited by 1
- Matroid.contract_closure_eqproof · cited by 1
- ZFSet.IsOrdinal.rank_injproof · cited by 1
- perfect_iff_eq_derivedSetproof · cited by 1
- Matroid.spanning_iff_ground_subset_closureproof · cited by 1