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Proof step 60 from proof lim-exists (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 61:
⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ )
Proof step 62:
# σσ = ∞, ii(0) = 0, mon(σσ), ∀ n. σσ[n] = σσ[0] + ⌜nf to ii(n)⌝ , ∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1), ∀ 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) ⊦ σσ = [], ∀ n. # σσ[0] ≠ ⌜n⌝ , ∃ n. # σσ[n] = ∞, ∃ n, σ1. (σσ[0] + ⌜nf⌝ to m) + σ1 = σσ[n]

Rule argument

spec: nat-inf name: notinf-fin seq: ⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ ) subst: [n∞] → [# σσ[0]] flags: <all paths>

Additional information

Used terms: # σσ[0]