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Proof step 13 from proof append-assoc (previous step)

⊦ (⌜x⌝ + ⌜x0⌝ ) + ⌜nf⌝ = ⌜λ n. (n < # x ⊃ x[n];(n - # x < # x0 ⊃ x0[n - # x];nf(n - # x - # x0)))⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
⊦ (⌜x⌝ + ⌜x0⌝ ) + ⌜nf⌝ = ⌜λ n. (n < # x ⊃ x[n];(n < # x0 + # x ⊃ x0[n - # x];nf(n - # x - # x0)))⌝

Rule argument

Additional information

Used simplifier rules: ls-01: n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; from specification nat%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat