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Proof step 3 from proof succlessleninv-invsize (previous step)

# nσ = ⌜inv(nσ)[n]⌝ + ⌜1⌝ , ⌜n⌝ + ⌜1⌝ < leninv(nσ), stutf(nσ) ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 4:
# nσ = ⌜inv(nσ)[n]⌝ + ⌜1⌝ , ⌜m⌝ = leninv(nσ), ⌜n⌝ + ⌜1⌝ < leninv(nσ), stutf(nσ) ⊦

Rule argument

term: leninv(nσ)

Additional information

Used simplifier rules: leninv-inf-strong: ⊦ stutf(nσ) → ( leninv(nσ) = ∞ ↔ # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]) ∧ (∀ m. ∃ m0. m < nσ[m0]));%natinf freely generated by ∞, ⌜ ⌝;;%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf% ⊦ n∞ = ⌜m⌝ + ⌜n⌝ → (n∞ = ∞ ↔ false); (s)