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Proof step 29 from proof inv-inverts-last (previous step)

# nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , stutf(nσ), n1 ≤ nσ[n] ⊦ ((λ m. max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = m).n) to n1)[nσ[n]] = n

User applied rule constructor cut

And obtained the following new goals

Proof step 30:
# nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , n1 = 0, stutf(nσ), n1 ≤ nσ[n] ⊦ ((λ m. max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = m).n) to n1)[nσ[n]] = n

Rule argument

var: n1

Additional information

Used simplifier rules: leninv-invlast: ⊦ # nσ = ⌜m⌝ + ⌜1⌝ ∧ leninv(nσ) = ⌜n⌝ + ⌜1⌝ ∧ stutf(nσ) → nσ[m] = n;%nat freely generated by 0, +1;;% ⊦ m +1 = m + 1; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%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% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s)%m < n ⊦ (nnf to n)[m] = nnf(m); (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)