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Proof step 33 from proof inv-inverts-leq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
leninv(nσ) = ⌜n0⌝ , nσ[n] < n0, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n < n, ⌜n⌝ < # nσ, stutf(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⌝ ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m⌝ ≠ ∞; (s)