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Proof step 17 from proof leq-leninv (previous step)

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

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, n, m] flags: current, []

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%l-02: ⊦ ¬ m + n < m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: nσ, n, m