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Proof step 132 from proof infinite-append-butlast (previous step)

lf(2 + n1) = a ' + x1, ii(n1 + 1) = m0 + 1, ii(0) = 0, ii(2 + n1) = 2 + m0 + # y, ((σ from m0 + 1) to # y) + ⌜(σ from m0 + 1)[# y] '⌝ = ⌜y⌝ + ⌜a '⌝ , ⌜# y⌝ + ⌜m0⌝ + ⌜1⌝ < # σ, ∀ n. n ≠ 0 → ii(n) ≠ 0, ∀ m, n. m ≤ n → ii(m) ≤ ii(n), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → (m = 0 ⊃ lf(0);lf(m).rest) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)) ⊦ σ[m0 + # y + 1] = a, # σ < ⌜2⌝ + ⌜m0⌝ + ⌜# y⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream inst: name: append-split seq: ⊦ finp(σ) ∧ # σ = # σ1 → (σ + σ0 = σ1 + σ2 ↔ σ = σ1 ∧ σ0 = σ2) subst: [σ2, σ1, σ0, σ] → [⌜a '⌝ , ⌜y⌝ , ⌜(σ from m0 + 1)[# y] '⌝ , (σ from m0 + 1) to # y] flags: rewrite

Additional information

Used terms: ⌜a '⌝ , ⌜y⌝ , ⌜(σ from m0 + 1)[# y] '⌝ , (σ from m0 + 1) to # y