Theorems · Theorem · order theory
trichotomous
∀ {α : Sort u_1} {r : α → α → Prop} [Std.Trichotomous r] (a b : α), r a b ∨ a = b ∨ r b a- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Std.Trichotomous
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by5
Results whose statement or proof uses this declaration.
- trichotomous_ofproof · cited by 9
- extensional_of_trichotomous_of_irreflproof · cited by 1
- Nat.sub_one_mul_sum_div_pow_eq_sub_sum_digitsproof · cited by 1
- Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digitsproof · cited by 1
- InitialSeg.eq_or_principalproof · cited by 0