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Proof step 194 from proof addarray-put-01 (previous step)

0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j ⊦ sk = j ', (addarray(r, ty, i0 + j + 1, st)[r -- sk]) = (addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk])

User applied rule case distinction

And obtained the following new goals

Proof step 142:
j = 0, 0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j ⊦ (addarray(r, ty, i0 + j + 1, st)[r -- sk]) = (addarray(r, ty, [] + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk]), sk = j '
Proof step 193:
j ≠ 0, 0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j ⊦ (addarray(r, ty, i0 + j + 1, st)[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk]), sk = j '

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]