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Proof step 137 from proof infinite-append-butlast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 138:
((σ from m0 + 1) to # y) + ⌜(σ from m0 + 1)[# y] '⌝ = ⌜y⌝ + ⌜a '⌝ , ii(n1 + 1) = m0 + 1, ii(0) = 0, ii(2 + n1) = 2 + m0 + # y, lf(2 + n1) = a ' + x1, ⌜# y⌝ + ⌜m0⌝ + ⌜1⌝ < # σ, (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → (m = 0 ⊃ lf(0);lf(m).tail) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)), ∀ n. n ≠ 0 → ii(n) ≠ 0, ∀ m, n. m ≤ n → ii(m) ≤ ii(n) ⊦ #((σ from m0 + 1) to # y) = ⌜# y⌝ , σ[m0 + # y + 1] = a, # σ < ⌜2⌝ + ⌜m0⌝ + ⌜# y⌝

Rule argument

Additional information

Used simplifier rules: ⊦ # ⌜x⌝ = ⌜# x⌝ ; (s)% ⊦ finp(σ to m); (s)