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Proof step 92 from proof infinite-append-prefixnextnli (previous step)

# lf(n0) = ii(n0), #((σ from ii(n0)) to # nextnli0(lf(n0), n0)) = ⌜# nextnli0(lf(n0), n0)⌝ , (σ from ii(n0))[n3] = nextnli0(lf(n0), n0)[n3], ii(0) = 0, lf(0) = [], n3 < # nextnli0(lf(n0), n0), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → nextnli0(lf(m), m) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)), ∀ n2. n2 < ii(n0) → lf(n0)[n2] = σ[n2], ∀ m, n. m ≤ n → ii(m) ≤ ii(n) ⊦ nextnli0(lf(n0), n0)[n3] = σ[n3 + ii(n0)], nextnli0(lf(n0), n0) = [], # σ < ⌜ii(n0)⌝ + ⌜# nextnli0(lf(n0), n0)⌝ , #(σ from ii(n0)) < ⌜# nextnli0(lf(n0), n0)⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 93:
# lf(n0) = ii(n0), (σ from ii(n0))[n3] = nextnli0(lf(n0), n0)[n3], ii(0) = 0, lf(0) = [], n3 < # nextnli0(lf(n0), n0), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → nextnli0(lf(m), m) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n2. n2 < ii(n0) → lf(n0)[n2] = σ[n2] ⊦ nextnli0(lf(n0), n0)[n3] = σ[n3 + ii(n0)], nextnli0(lf(n0), n0) = [], #(σ from ii(n0)) < ⌜# nextnli0(lf(n0), n0)⌝ , # σ < ⌜ii(n0)⌝ + ⌜# nextnli0(lf(n0), n0)⌝

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s)%¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ ; (s)