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Proof step 55 from proof inv-get-inverse-succ (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
stutf(nσ), ⌜n⌝ < leninv(nσ), ⌜((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n)[n]⌝ + ⌜1⌝ < # nσ ⊦ leninv(nσ) = ∞, nσ[((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n)[n] + 1] = n + 1

Rule argument

Additional information

Used simplifier rules: sel-fin: ⊦ ⌜nl⌝ [n] = nl[n]; from specification stream[natstream]