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Proof step 4 from proof inv-inverts-last (previous step)

stutf(nσ), # nσ = ⌜n⌝ + ⌜1⌝ , stutf(nσ) ⊦ (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ to leninv(nσ).n)[nσ[n]] = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# nσ = ⌜n⌝ + ⌜1⌝ , stutf(nσ) ⊦ (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = m).n⌝ ;⌜(λ m. max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = m).n) to leninv(nσ).n⌝ )[nσ[n]] = n

Rule argument

Additional information

Used simplifier rules: to-inf: ⊦ ⌜nnf⌝ to n = ⌜nnf to n⌝ ; from specification stream[natstream]%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%inf-inseq-reduce: ⊦ n∞ = ⌜m⌝ + ⌜n0⌝ → (⌜n⌝ < n∞ ↔ n < m + n0); from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf