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Proof step 44 from proof inv-get-inverse (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
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: 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%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat