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Proof step 32 from proof inv-inverts-leq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
leninv(nσ) = ⌜n0⌝ , nσ[n] < n0, ⌜n⌝ < # nσ, stutf(nσ), max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n < n ⊦

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%get-infto: m < n ⊦ (nnf to n)[m] = nnf(m); from specification stream[natstream]%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic