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Proof step 10 from proof inv-get-lslen (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
n∞ ≠ ∞ ⊦ ⌜n∞.n⌝ = n∞
Proof step 12:
leninv(nσ) = ⌜n0⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ∞, n < n0, stutf(nσ) ⊦ ⌜max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n⌝ < # nσ
Proof step 33:
leninv(nσ) = ⌜n0⌝ , n < n0, stutf(nσ) ⊦ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ∞, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) < # nσ

Rule argument

spec: nat-inf name: fin-inject-embed 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)