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Proof step 12 from proof subarray-append-shift-left (previous step)

# ar0 = n0 + n, n1 < n0 + # ar1, n + n1 < # ar0 + # ar1 ⊦ (n + n1 < # ar0 ⊃ ar0[n + n1];ar1[n + n1 - # ar0]) = (subarray(ar0, n, n0) + ar1)[n1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# ar0 = n0 + n, n1 < n0 + # ar1 ⊦ (n1 < n0 ⊃ ar0[n + n1];ar1[n1 - n0]) = (subarray(ar0, n, n0) + ar1)[n1]

Rule argument

Additional information

Used simplifier rules: ⊦ m + n - n + n1 = m - n1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic