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Proof step 152 from proof inv-ls-succ (previous step)

nσ[n0] = nσ[n2] + 1, leninv(nσ) = ⌜n1⌝ , ⌜n0⌝ < # nσ, n0 ≤ n2, stutf(nσ), nσ[n0] < n1, ⌜n2⌝ < # nσ, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = nσ[n0] → ¬ n0 < m, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = nσ[n2] → ¬ n2 < m ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, n0, n2] flags: current, []

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%eq: ⊦ m = n + 1 → ¬ m ≤ n; from specification nat Used terms: nσ, n0, n2