wellFounded_of_finite — Mathlib

English

Under IsTrichotomous α r and hr, well-foundedness of Lex r s holds given WellFounded of r swapped and bottom condition.

Русский

При IsTrichotomous α r и hr сохраняется хорошо основанность Lex r s при условии замены и ноля.

LaTeX

$$$WellFounded (Finsupp.Lex r s)$$$

Lean4

theorem wellFounded_of_finite [IsStrictTotalOrder α r] [Finite α] (hs : WellFounded s) :
    WellFounded (Finsupp.Lex r s) :=
  InvImage.wf (@equivFunOnFinite α N _ _) (Pi.Lex.wellFounded r fun _ => hs)

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