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Proof step 13 from proof addarray-put-01 (previous step)

0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j ⊦ (r -- j ' ∈ st ∨ ¬ n→i(# ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j))))) + i0 < 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 4:
0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j ⊦ r -- j ' ∈ st ∨ ¬ n→i(# ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j))))) + i0 < j
Proof step 12:
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 '])

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]