English
A well-founded on fiber construction for a sigma-lex order yields well-foundedness on the product when base is well-founded and fibers are well-founded.
Русский
Построение через сигма-лекс с волокнами обеспечивает хорошо основанное произведение при условии базового хорошо основанного и волокон.
LaTeX
$$WellFounded (Sigma.Lex rι rπ on fun c => ⟨f c, g (f c) c⟩)$$
Lean4
/-- A well quasi-order or WQO is a relation such that any infinite sequence contains an infinite
monotonic subsequence, or equivalently, two elements `f m` and `f n` with `m < n` and
`r (f m) (f n)`.
For a preorder, this is equivalent to having a well-founded order with no infinite antichains.
Despite the nomenclature, we don't require the relation to be preordered. Moreover, a well
quasi-order will not in general be a well-order. -/
def WellQuasiOrdered (r : α → α → Prop) : Prop :=
∀ f : ℕ → α, ∃ m n : ℕ, m < n ∧ r (f m) (f n)
