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Proof step 38 from proof lim-exists (previous step)

# σσ = ∞, # x = ii(n), # σσ[n] = ⌜n0⌝ , ii(0) = 0, mon(σσ), ∀ m. n ≤ m → lf(m) = [] ∧ ii(m) = ii(n), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ 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), ∀ m. n ≤ m → σσ[m] = σσ[n] ⊦ σσ = [], n0 < m, ∃ n. # σσ[n] = ∞, ∃ n0, σ1. (σσ[n] to m) + σ1 = σσ[n0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
# σσ[n] = ⌜n0⌝ , # x = ii(n), # σσ = ∞, ii(0) = 0, mon(σσ), m ≤ n0, ∀ m. n ≤ m → σσ[m] = σσ[n], ∀ n0. ii(n0 + 1) = ii(n0) + # lf(n0) ∧ ¬ ii(n) < ii(n0 + 1) ∧ (x from ii(n0)) to # lf(n0) = lf(n0), ∀ n. σσ[n + 1] = σσ[n] + ⌜lf(n)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ m. n ≤ m → lf(m) = [] ∧ ii(m) = ii(n) ⊦ σσ = [], ∃ n0, σ1. (σσ[n] to m) + σ1 = σσ[n0], ∃ n. # σσ[n] = ∞

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)