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Proof step 102 from proof inv-get-inverse-between (previous step)

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