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Proof step 34 from proof inv-get-lslen (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ )
Proof step 36:
leninv(nσ) = ⌜n0⌝ , n < n0, stutf(nσ) ⊦ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) < # nσ, ∀ n0. max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) ≠ ⌜n0⌝

Rule argument

spec: nat-inf name: notinf-fin seq: ⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ ) subst: [n∞] → [max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n)] flags: <all paths>

Additional information

Used terms: max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n)