Theorems · Theorem · order theory
lt_or_gt_of_ne
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, a ≠ b → a < b ∨ b < a- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 11 from the axioms · 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_trichotomyproof · cited by 178
Cited by41
Results whose statement or proof uses this declaration.
- Ne.lt_or_gtproof · cited by 108
- ne_iff_lt_or_gtproof · cited by 7
- IsAddIndecomposable.mem_or_neg_mem_closure_baseOfproof · cited by 5
- Ordinal.isPrincipal_add_of_isPrincipal_mulproof · cited by 3
- Real.tendsto_div_pow_mul_exp_add_atTopproof · cited by 3
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- StrictConvexOn.secant_strict_monoproof · cited by 3
- ConvexOn.secant_monoproof · cited by 3
- exists_pair_ltproof · cited by 3
- Set.preimage_mul_const_uIccproof · cited by 3
- IsUltrametricDist.isOpen_closedBallproof · cited by 3
- ArchimedeanClass.mk_sumproof · cited by 2