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Proof step 123 from proof inv-ls-succ (previous step)

leninv(nσ) ≠ ∞, ⌜(λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n⌝ [n + 1] ≤ (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], max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) = ⌜n0⌝ , stutf(nσ), ⌜n⌝ + ⌜1⌝ < leninv(nσ) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 124:
max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) = ⌜n0⌝ , stutf(nσ), ⌜n⌝ + ⌜1⌝ < leninv(nσ), ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n)[n + 1] ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n)[n] ⊦ leninv(nσ) = ∞

Rule argument

Additional information

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