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Proof step 32 from proof inv-inverts-leq (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
leninv(nσ) = ⌜n0⌝ , ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n0)[nσ[n]] < n, ⌜nσ[n]⌝ < leninv(nσ), ⌜n⌝ < # nσ, stutf(nσ) ⊦ 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