Theorems · Theorem · order theory
cmp_eq_cmp_symm
∀ {α : Type u_1} [inst : LinearOrder α] {x y : α} {β : Type u_3} [inst_1 : LinearOrder β] {x' y' : β},
cmp x y = cmp x' y' ↔ cmp y x = cmp y' x'- Defined in
- Mathlib.Order.Compare
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- LinearOrderLinearOrder
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.
- LinearOrderstatement and proof · cited by 8,572
- cmpstatement and proof · cited by 43
- cmp_swapproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- le_iff_le_of_cmp_eq_cmpproof · cited by 2
- eq_iff_eq_of_cmp_eq_cmpproof · cited by 1
- UpperHalfPlane.lt_dist_iff_lt_dist_coe_centerproof · cited by 0
- UpperHalfPlane.le_dist_iff_le_dist_coe_centerproof · cited by 0