Theorems · Theorem · order theory
eq_iff_eq_of_cmp_eq_cmp
∀ {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' → (x = y ↔ x' = y')- Defined in
- Mathlib.Order.Compare
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- LinearOrderLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- le_antisymm_iffproof · cited by 62
- cmpstatement and proof · cited by 43
- cmp_eq_cmp_symmproof · cited by 4
- le_iff_le_of_cmp_eq_cmpproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- UpperHalfPlane.dist_eq_iff_dist_coe_center_eqproof · cited by 3