Theorems · Theorem · logic and foundations
Std.Symm.iff
∀ {α : Type u_1} {r : α → α → Prop} [Std.Symm r] (x y : α), r x y ↔ r y x- Defined in
- Mathlib.Logic.Relation
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- Std.Symm
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- symm_ofproof · cited by 12
Cited by8
Results whose statement or proof uses this declaration.
- Set.pairwise_insert_of_symmproof · cited by 10
- SimpleGraph.adj_commproof · cited by 10
- Set.pairwise_insert_of_symm_of_notMemproof · cited by 6
- Std.Symm.flip_eqproof · cited by 4
- Rel.swap_mem_interedges_iffproof · cited by 3
- SimpleGraph.Subgraph.adj_commproof · cited by 2
- SimpleGraph.isClique_iff_isChain_adjproof · cited by 0
- Symmetric.iffproof · cited by 0