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Proof step 15 from proof lsleninv-1 (previous step)

m1 + 1 < nσ[m], m1 < n, n < nσ[m], ⌜m⌝ < # nσ, m1 < nσ[m], stutf(nσ), (# nσ = ∞ ⊃ nσ[m2] = m1 ∧ (∀ m0. m2 < m0 → nσ[m0] = nσ[m2] + 1);nσ[(# nσ).n - 1] = m1) ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 16:
⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n)
Proof step 17:
m1 < nσ[m], ⌜m⌝ < # nσ, n < nσ[m], m1 < n, m1 + 1 < nσ[m], stutf(nσ), stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n), (# nσ = ∞ ⊃ nσ[m2] = m1 ∧ (∀ m0. m2 < m0 → nσ[m0] = nσ[m2] + 1);nσ[(# nσ).n - 1] = m1) ⊦

Rule argument

spec: <toplevel> name: stutf-alltaken seq: ⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n) subst: [nσ, m, n] → [nσ, m, n]

Additional information

Used terms: nσ, m, n