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Proof step 7 from proof succlessleninv-invsize (previous step)

# nσ = ⌜inv(nσ)[n]⌝ + ⌜1⌝ , ⌜m0⌝ + ⌜1⌝ = leninv(nσ), n < m0, stutf(nσ) ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: monls-ls seq: ⊦ mon<(nσ) ∧ m < n ∧ ⌜n⌝ < # nσ → nσ[m] < nσ[n] subst: [nσ, m, n] → [inv(nσ), n, m0]

Additional information

Used simplifier rules: stutf-invmonls: ⊦ stutf(nσ) → (mon<(inv(nσ)) ↔ true);%leninv-is-len-inv: ⊦ stutf(nσ) → # inv(nσ) = leninv(nσ);%leninv-invlast-inv: ⊦ # nσ = ⌜m⌝ + ⌜1⌝ ∧ leninv(nσ) = ⌜n⌝ + ⌜1⌝ ∧ stutf(nσ) → inv(nσ)[n] = m;%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⌝ + ⌜n0⌝ → (⌜n⌝ < n∞ ↔ n < m + n0); (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: inv(nσ), n, m0