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Proof step 11 from proof infinite-append-prefixnextli-weak (previous step)

ii(0) = 0, lf(0) = [], ∀ n. ii(n + 1) = ii(n) + # nextli0(lf(n)) ∧ ¬ # σ < ⌜ii(n + 1)⌝ ∧ (σ from ii(n)) to # nextli0(lf(n)) = ⌜nextli0(lf(n))⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n + 1) = nextli(lf(n)), ∀ x. nextli(x) = x + nextli0(x), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → nextli0(lf(m)) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)) ⊦ ii(0) = 0 ∧ (∀ n. ii(n) ≤ ii(n + 1) ∧ ¬ # σ < ⌜ii(n + 1)⌝ ∧ σ to ii(n + 1) = ⌜nextli((σ to ii(n)).l)⌝ ) ∧ (∀ m, n. m ≤ n → ii(m) ≤ ii(n)) ∧ (finp(σ) ⊃ ∃ n. # σ = ⌜ii(n)⌝ ∧ ⌜nextli(σ.l)⌝ = σ ∧ (∀ m. n ≤ m → ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
ii(0) = 0, lf(0) = [], ∀ n. ii(n + 1) = ii(n) + # nextli0(lf(n)) ∧ ¬ # σ < ⌜ii(n + 1)⌝ ∧ (σ from ii(n)) to # nextli0(lf(n)) = ⌜nextli0(lf(n))⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n + 1) = nextli(lf(n)), ∀ x. nextli(x) = x + nextli0(x), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → nextli0(lf(m)) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)) ⊦ ii(n0) ≤ ii(n0 + 1) ∧ ¬ # σ < ⌜ii(n0 + 1)⌝ ∧ σ to ii(n0 + 1) = ⌜nextli((σ to ii(n0)).l)⌝ ∧ (finp(σ) ⊃ ∃ n. # σ = ⌜ii(n)⌝ ∧ ⌜nextli(σ.l)⌝ = σ ∧ (∀ m. n ≤ m → ii(m) = ii(n));∃ m. ii(m) ≤ n1 ∧ n1 < ii(m + 1))

Proof step 11 from proof infinite-append-prefixnextli-weak (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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