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Proof step 43 from proof inv-get-inverse-between (previous step)

nσ[n0] = n + 1, # nσ = ∞, max∞(λ n0. nσ[n0] = n) = ⌜n1⌝ , nσ[m0] = n + 1, m0 < n0, m1 < n0, n1 + m + 1 < ∞.n, stutf(nσ), ⌜n⌝ + ⌜1⌝ < leninv(nσ), m0 < m1, n + 1 < nσ[m1], m0 + 1 < n0, ∀ m. ∃ m0. m < nσ[m0] ⊦ n0 = 0, nσ[n1 + m + 1] = n + 1, ∞.n = 0, m1 = 0, nσ[m1] = 0

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, m1, n0] flags: current, []

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%lels-03: ⊦ m < n → m ≤ n; from specification nat%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: nσ, m1, n0