Theorems · Theorem · order theory
trichotomous_of
∀ {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
- 9 results in Mathlib
- Foundations
- Depth 12 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.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- trichotomousproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- Ordinal.exists_ord_cof_eqproof · cited by 5
- isChain_of_trichotomousproof · cited by 4
- Finset.Colex.IsInitSeg.totalproof · cited by 1
- IsAntichain.subsingletonproof · cited by 1
- injective_of_increasingproof · cited by 1
- ZFSet.isOrdinal_iff_trichotomousproof · cited by 1
- trans_trichotomous_leftproof · cited by 0
- trans_trichotomous_rightproof · cited by 0
- SimpleGraph.nonuniformWitness_specproof · cited by 0