psigma_revLex — Mathlib

English

The reverse-lexicographic well-foundedness holds for PSigma with base WellFounded relations.

Русский

Обратный лексикографический порядок на PSigma хорошо основан при базовом WellFounded.

LaTeX

$$$[\\text{WellFounded } r] \\Rightarrow [\\text{WellFounded } s] \\Rightarrow \\text{WellFounded } (PSigma.RevLex r s)$$$

Lean4

theorem psigma_revLex {α : Sort*} {β : Sort*} {r : α → α → Prop} {s : β → β → Prop} (ha : WellFounded r)
    (hb : WellFounded s) : WellFounded (RevLex r s) :=
  WellFounded.intro fun ⟨a, b⟩ => revLexAccessible (apply hb b) (WellFounded.apply ha) a

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