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Proof step 80 from proof inv-get-inverse (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 81:
leninv(nσ) = ⌜n0⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ⌜n1⌝ , n < n0, stutf(nσ) ⊦ nσ[n1] = n, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ∞

Rule argument

spec: nat-inf name: elim seq: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ) subst: [n∞, m] → [max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n), m]

Additional information

Used simplifier rules: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ); (elim) Used terms: max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n), m