Theorems · Definition · order theory
SetRel.IsSymm
{α : Type u_1} → SetRel α α → PropA relation R is symmetric if a ~[R] b ↔ b ~[R] a.
- Defined in
- Mathlib.Data.Rel
- Cited by
- 93 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 10 definitions · uses no axioms
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.
- SetRelstatement and proof · cited by 581
Cited by95
Results whose statement or proof uses this declaration.
- comp_symm_mem_uniformity_setsstatement · cited by 18
- SetRel.symmstatement and proof · cited by 13
- UniformSpace.mem_ball_symmetrystatement and proof · cited by 9
- comp_symm_of_uniformityproof · cited by 7
- SetRel.commstatement and proof · cited by 5
- IsUltraUniformity.hasBasisstatement · cited by 5
- SetRel.inv_eq_selfstatement and proof · cited by 5
- UniformSpace.hasBasis_symmetricstatement · cited by 5
- nhds_le_uniformityproof · cited by 5
- IsUltraUniformity.mk_of_hasBasisstatement and proof · cited by 4
- uniformity_hasBasis_closedproof · cited by 4
- uniformity_hasBasis_open_symmetricstatement · cited by 4