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Proof step 9 from proof inv-get-lslen (previous step)

leninv(nσ) = ⌜n0⌝ , ⌜n⌝ < leninv(nσ), stutf(nσ) ⊦ leninv(nσ) = ∞, ⌜((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n0)[n]⌝ < # nσ

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
leninv(nσ) = ⌜n0⌝ , n < n0, stutf(nσ) ⊦ ⌜max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n⌝ < # nσ

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%m < n ⊦ (nnf to n)[m] = nnf(m); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)