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Proof step 84 from proof leninv-succ (previous step)

# nσ = ∞, nσ[m] < nσ[m1], m1 < m2, stutf(nσ), ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1 ⊦ nσ[m2] = nσ[m1]

User applied rule insert lemma

And obtained the following new goals

Proof step 85:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]
Proof step 86:
# nσ = ∞, m1 < m2, nσ[m] < nσ[m1], stutf(nσ), mon≤(nσ) ∧ m1 ≤ m ∧ ⌜m⌝ < # nσ → nσ[m1] ≤ nσ[m], ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1 ⊦ nσ[m2] = nσ[m1]

Rule argument

spec: <toplevel> name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, m1, m]

Additional information

Used terms: nσ, m1, m