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Proof step 3 from proof subarray-append-shift-left (previous step)

n + m = # ar0 + # ar1, n ≤ # ar0 ⊦ subarray(ar0 + ar1, n, m) = subarray(ar0, n, # ar0 - n) + ar1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# ar0 = n0 + n, n + m = # ar0 + # ar1, n ≤ # ar0 ⊦ subarray(ar0 + ar1, n, m) = subarray(ar0, n, n0) + ar1

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# ar0, n, n0]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # ar0, n, n0