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Proof step 81 from proof inv-get-inverse-between (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 82:
leninv(nσ) = ⌜n0⌝ , ⌜n⌝ + ⌜1⌝ < leninv(nσ), ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n0)[n] + m + 1 < ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n0)[n + 1], stutf(nσ) ⊦ nσ[((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n0)[n] + m + 1] = n + 1, leninv(nσ) = ∞

Rule argument

spec: nat-inf name: elim seq: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ) subst: [n∞, m] → [leninv(nσ), m0]

Additional information

Used simplifier rules: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ); (elim) Used terms: leninv(nσ), m0