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Proof step 117 from proof inv-ls-succ (previous step)

max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ⌜n1⌝ , nσ[n0] = n + 1, leninv(nσ) = ∞, ⌜n0⌝ < # nσ, stutf(nσ), n0 ≤ n1, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m ⊦ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ∞

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 118:
leninv(nσ) = ∞, nσ[n0] = n + 1, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ⌜n1⌝ , n0 ≤ n1, stutf(nσ), ⌜n0⌝ < # nσ, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m ⊦

Rule argument

Additional information

Used simplifier rules: disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic