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Proof step 16 from proof less-leninv (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 17:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]
Proof step 18:
# nσ = ∞, nσ[n + 1] = nσ[n] + 1, nσ[m] < nσ[n], stutf(nσ), m < n → nσ[n] = nσ[m] + 1, mon≤(nσ) ∧ n ≤ m ∧ ⌜m⌝ < # nσ → nσ[n] ≤ nσ[m], ∀ m1. m < m1 → nσ[m1] = nσ[m] + 1 ⊦

Rule argument

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

Additional information

Used terms: nσ, n, m