Theorems · Theorem · order theory
Ne.lt_or_gt
∀ {α : Type u_2} [inst : LinearOrder α] {a b : α}, a ≠ b → a < b ∨ b < a- Defined in
- Mathlib.Order.Basic
- Cited by
- 108 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 30 definitions · uses no axioms
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- lt_or_gt_of_neproof · cited by 41
Cited by108
Results whose statement or proof uses this declaration.
- closure_Iooproof · cited by 20
- mul_self_posproof · cited by 17
- bernoulli_eq_bernoulli'_of_ne_oneproof · cited by 10
- Set.OrdConnected.strictConvexproof · cited by 9
- interior_closedBallproof · cited by 8
- InnerProductSpace.gramSchmidt_orthogonalproof · cited by 6
- ArchimedeanClass.stdPart_eq_zeroproof · cited by 6
- intervalIntegral.continuousWithinAt_primitiveproof · cited by 6
- ENNReal.mul_rpow_eq_iteproof · cited by 5
- Real.add_one_lt_expproof · cited by 4
- Real.contDiffAt_rpow_of_neproof · cited by 4
- ENNReal.inv_rpowproof · cited by 3