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Proof step 26 from proof stutf-maxinf-is-fin (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 27:
⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n)
Proof step 28:
stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ m ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = m), ∀ n. ¬ ⌜n⌝ < # nσ ∨ nσ[n] ≠ m, stutf(nσ) ⊦ # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m) ∨ (∀ n. ⌜n⌝ < # nσ → nσ[n] < 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, m, m] flags: current, []

Additional information

Used terms: nσ, m, m