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Proof step 48 from proof lim-exists (previous step)

# σσ[n] = ⌜n0⌝ , ii(0) = 0, # σσ = ∞, # x = ii(n), ii(m0 + 1) = ii(m0) + # lf(m0), (x from ii(m0)) to # lf(m0) = lf(m0), mon(σσ), n ≤ m0 + 1, ii(m0 + 1) ≤ ii(n), ∀ m. n ≤ m → lf(m) = [] ∧ ii(m) = ii(n), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), σσ[m0 + 1] = σσ[m0] + ⌜lf(m0)⌝ , ∀ n. σσ[n + 1] = σσ[n] + ⌜lf(n)⌝ , ∀ n0. ii(n0 + 1) = ii(n0) + # lf(n0) ∧ ¬ ii(n) < ii(n0 + 1) ∧ (x from ii(n0)) to # lf(n0) = lf(n0), n ≤ m0 → σσ[m0] = σσ[n] ⊦ σσ = [], σσ[m0 + 1] = σσ[n], ∃ n. # σσ[n] = ∞

User applied rule all left

And obtained the following new goals

Proof step 49:
# σσ[n] = ⌜n0⌝ , ii(0) = 0, # σσ = ∞, # x = ii(n), ii(m0 + 1) = ii(m0) + # lf(m0), (x from ii(m0)) to # lf(m0) = lf(m0), mon(σσ), n ≤ m0 + 1, ii(m0 + 1) ≤ ii(n), n ≤ m0 → lf(m0) = [] ∧ ii(m0) = ii(n), ∀ m. n ≤ m → lf(m) = [] ∧ ii(m) = ii(n), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), σσ[m0 + 1] = σσ[m0] + ⌜lf(m0)⌝ , ∀ n. σσ[n + 1] = σσ[n] + ⌜lf(n)⌝ , ∀ n0. ii(n0 + 1) = ii(n0) + # lf(n0) ∧ ¬ ii(n) < ii(n0 + 1) ∧ (x from ii(n0)) to # lf(n0) = lf(n0), n ≤ m0 → σσ[m0] = σσ[n] ⊦ σσ = [], σσ[m0 + 1] = σσ[n], ∃ n. # σσ[n] = ∞

Rule argument

pos: left 10 terms: m0 abort: F discard: F computed: F

Additional information

Used terms: m0