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Proof step 22 from proof inv-ls-succ (previous step)

# nσ = ∞, nσ[n0] = n + 1, nσ[n1] = n + 1, n0 < n1, n0 < m, n + 1 < nσ[m], m < n1, n0 + 1 < n1, stutf(nσ), ∞.n ≤ max∞(λ n0. nσ[n0] = n).n, ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0], ∀ n0. ∃ n1. n0 < n1 ∧ nσ[n1] = n + 1 ⊦ n0 = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 23:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]

Rule argument

spec: <toplevel> name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, m, n1]

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (mon≤(nσ) ↔ true);% ⊦ m < n → m ≤ n; (s)% ⊦ ⌜m⌝ < ∞; (s)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: nσ, m, n1