Theorems · Theorem · order theory
lt_trichotomy
∀ {α : Type u_1} [inst : LinearOrder α] (a b : α), a < b ∨ a = b ∨ b < a- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 178 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 29 definitions · uses no axioms
- Assumes
- LinearOrder
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
- lt_or_geproof · cited by 182
- Decidable.lt_or_eq_of_le'proof · cited by 5
Cited by178
Results whose statement or proof uses this declaration.
- abs_posproof · cited by 45
- lt_or_gt_of_neproof · cited by 41
- ENNReal.rpow_mulproof · cited by 33
- sign_mulproof · cited by 11
- max_def'proof · cited by 7
- CharP.intCast_eq_zero_iffproof · cited by 7
- one_lt_mabsproof · cited by 6
- variationOnFromTo.eq_neg_swapproof · cited by 6
- Affine.Simplex.ExcenterExists.dist_excenterproof · cited by 6
- ENNReal.rpow_negproof · cited by 6
- cmp_comparesproof · cited by 5
- ENNReal.continuous_rpow_constproof · cited by 5