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Proof step 32 from proof eq-leninv (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 33:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]
Proof step 34:
# nσ = ∞, nσ[m2] + 1 = nσ[n], n < m0, stutf(nσ), mon≤(nσ) ∧ n ≤ m0 ∧ ⌜m0⌝ < # nσ → nσ[n] ≤ nσ[m0], ∀ m1. m2 < m1 → nσ[m1] = nσ[n] ⊦ nσ[m0] = nσ[n]

Rule argument

spec: <toplevel> name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, n, m0]

Additional information

Used terms: nσ, n, m0