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Proof step 12 from proof addarray-put-01 (previous step)

0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j ⊦ val = (addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- j '])

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 5:
⊦ (addarray(r, ty, val ' + vals, st)[r -- 0 ']) = val
Proof step 11:
j ≠ 0, 0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j ⊦ val = (addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- j '])

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ [] + vals = vals], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1])]]