English
Another formulation equating the trichotomy result with branch-values via an explicit disjunction.
Русский
Ещё одно формулирование через дизъюнкцию значений ветвей тричитотомии.
LaTeX
$$$ Eq(ltTrichotomy x y p q r, s) \\iff (x < y \\land p = s) \\lor (x = y \\land q = s) \\lor (y < x \\land r = s) $$$
Lean4
@[deprecated lt_trichotomy (since := "2025-04-21")]
theorem ltTrichotomy_eq_iff : ltTrichotomy x y p q r = s ↔ (x < y ∧ p = s) ∨ (x = y ∧ q = s) ∨ (y < x ∧ r = s) :=
by
refine ltByCases x y (fun h => ?_) (fun h => ?_) (fun h => ?_)
· simp only [ltTrichotomy_lt, false_and, true_and, or_false, h, h.not_gt, h.ne]
· simp only [ltTrichotomy_eq, false_and, true_and, or_false, false_or, h, lt_irrefl]
· simp only [ltTrichotomy_gt, false_and, true_and, false_or, h, h.not_gt, h.ne']
