ltTrichotomy_ne — Mathlib

English

The trichotomy relation is symmetric under swapping the two arguments and corresponding branches: ltTrichotomy x y p q r = ltTrichotomy y x r q p.

Русский

Тризначная разбивка симметрична при обмене аргументов: ltTrichotomy x y p q r = ltTrichotomy y x r q p.

LaTeX

$$$ ltTrichotomy x y p q r = ltTrichotomy y x r q p $$$

Lean4

@[deprecated lt_trichotomy (since := "2025-04-21")]
theorem ltTrichotomy_ne (h : x ≠ y) : ltTrichotomy x y p q r = if x < y then p else r :=
  ltByCases_ne h

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