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Proof step 27 from proof stutf-maxinf-is-fin (previous step)

stutf(nσ), ∀ n. ¬ ⌜n⌝ < # nσ ∨ nσ[n] ≠ m ⊦ ∀ n. ⌜n⌝ < # nσ → nσ[n] < m, # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m)

User applied rule insert lemma

And obtained the following new goals

Proof step 28:
⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n)
Proof step 29:
stutf(nσ), stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ m ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = m), ∀ n. ¬ ⌜n⌝ < # nσ ∨ nσ[n] ≠ m ⊦ ∀ n. ⌜n⌝ < # nσ → nσ[n] < m, # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m)

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, m]

Additional information

Used terms: nσ, m, m