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Proof step 45 from proof inv-get-inverse (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
leninv(nσ) = ⌜n0⌝ , n < n0, stutf(nσ) ⊦ nσ[max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n] = n

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⌝ ↔ m < n; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)