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Proof step 72 from proof lim-exists (previous step)

# σσ = ∞, # σσ[0] = ⌜n⌝ , σσ[m0] = σσ[0] + ⌜nf to ii(m0)⌝ , σσ[m0 + 1] = σσ[0] + ⌜nf to ii(m0 + 1)⌝ , ii(0) = 0, m < ii(m0 + 1) + n, ii(m0) < ii(m0 + 1), mon(σσ), ii(m0) + n ≤ m, n ≤ m, ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. σσ[n + 1] = σσ[n] + ⌜lf(n)⌝ , ∀ n. ii(n + 1) = ii(n) + # lf(n) ∧ (nf from ii(n)) to # lf(n) = lf(n) ⊦ ii(m0 + 1) + n = 0, ii(m0 + 1) = 0, σσ = [], ∃ n. # σσ[n] = ∞, ∃ n, σ1. (σσ[0] + ⌜nf⌝ to m) + σ1 = σσ[n]

User applied rule exists right

And obtained the following new goals

Proof step 73:
# σσ[0] = ⌜n⌝ , # σσ = ∞, σσ[m0 + 1] = σσ[0] + ⌜nf to ii(m0 + 1)⌝ , σσ[m0] = σσ[0] + ⌜nf to ii(m0)⌝ , ii(0) = 0, ii(m0) < ii(m0 + 1), m < ii(m0 + 1) + n, mon(σσ), n ≤ m, ii(m0) + n ≤ m, ∀ n. ii(n + 1) = ii(n) + # lf(n) ∧ (nf from ii(n)) to # lf(n) = lf(n), ∀ n. σσ[n + 1] = σσ[n] + ⌜lf(n)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n) ⊦ ii(m0 + 1) + n = 0, (σσ[0] + ⌜nf⌝ to m) + ((⌜nf⌝ to ii(m0 + 1)) from (m - n)) = σσ[m0 + 1], ii(m0 + 1) = 0, σσ = [], ∃ n. # σσ[n] = ∞

Rule argument

pos: right 5 terms: m0 + 1, (⌜nf⌝ to ii(m0 + 1)) from (m - n) abort: F discard: T computed: F

Additional information

Used terms: m0 + 1, (⌜nf⌝ to ii(m0 + 1)) from (m - n)