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Proof step 73 from proof lim-exists (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 74:
m = n0 + n, # σσ = ∞, ii(0) = 0, # σσ[0] = ⌜n⌝ , σσ[m0] = σσ[0] + ⌜nf to ii(m0)⌝ , σσ[m0 + 1] = σσ[0] + ⌜nf to ii(m0 + 1)⌝ , m < ii(m0 + 1) + n, ii(m0) + n ≤ m, n ≤ m, mon(σσ), ii(m0) < ii(m0 + 1), ∀ 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 = [], ii(m0 + 1) = 0, (σσ[0] + ⌜nf⌝ to m) + ⌜(nf to ii(m0 + 1)) from n0⌝ = σσ[m0 + 1], ∃ n. # σσ[n] = ∞

Rule argument

spec: nat inst: name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [m, n, n0] flags:

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m, n, n0