Theorems · Theorem · logic and foundations
Set.Subset.antisymm_iff
∀ {α : Type u} {a b : Set α}, a = b ↔ a ⊆ b ∧ b ⊆ a- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.Subset.antisymmproof · cited by 213
- Eq.subsetproof · cited by 124
Cited by4
Results whose statement or proof uses this declaration.
- Set.subset_empty_iffproof · cited by 40
- Set.eq_singleton_iff_unique_memproof · cited by 20
- Topology.IsCoinducing.isConnected_preimage_of_isClosedproof · cited by 3
- Set.surjective_codRestrictproof · cited by 1