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Proof step 3 from proof lsleninv-2 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: lsleninv-1 seq: ⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n < nσ[m] → (⌜n⌝ < leninv(nσ) ↔ true) subst: [nσ, m, n] → [nσ, m, n]

Additional information

Used simplifier rules: 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: nσ, m, n