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Proof step 9 from proof stutf-maxinf-is-fin (previous step)

# nσ = ∞, m ≤ nσ[n], stutf(nσ), ∀ n1. ∃ n0. n1 < n0 ∧ nσ[n0] = m ⊦ ∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m

User applied rule insert lemma

And obtained the following new goals

Proof step 10:
⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n)
Proof step 11:
stutf(nσ) ∧ ⌜n⌝ < # nσ ∧ m ≤ nσ[n] → (∃ m0. m0 ≤ n ∧ nσ[m0] = m), # nσ = ∞, m ≤ nσ[n], stutf(nσ), ∀ n1. ∃ n0. n1 < n0 ∧ nσ[n0] = m ⊦ ∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m

Rule argument

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

Additional information

Used terms: nσ, n, m