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Theorem KoenigsLemma-aux

isroot(g)(a), haspathanylength(g)(a), ∀ x. x ≠ [] ∧ pathp(g)(⌜x⌝ ) ∧ haspathanylength(g)(x.last) → (∃ b. cf(x) = x + b ') ∧ pathp(g)(⌜cf(x)⌝ ) ∧ haspathanylength(g)(cf(x).last) ⊦ # ((cf ^ n))(a ') = n + 1 ∧ haspathanylength(g)(((cf ^ n))(a ').last) ∧ pathp(g)(⌜((cf ^ n))(a ')⌝ )

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