Theorems · Theorem · order theory
ne_iff_lt_or_gt
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, a ≠ b ↔ a < b ∨ b < a- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- ne_of_gtproof · cited by 637
- ne_of_ltproof · cited by 203
- lt_or_gt_of_neproof · cited by 41
Cited by7
Results whose statement or proof uses this declaration.
- lt_or_lt_iff_neproof · cited by 13
- Valuation.IsNontrivial.exists_lt_oneproof · cited by 4
- Valuation.isEquiv_iff_val_lt_oneproof · cited by 3
- Real.continuousAt_rpow_of_neproof · cited by 2
- Matrix.submatrix_succAbove_det_eq_negOnePow_submatrix_succAbove_detproof · cited by 1
- Complex.re_neg_ne_zero_of_re_posproof · cited by 1
- Polynomial.IsEisensteinAt.coeff_memproof · cited by 0