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Proof step 228 from proof putarray-addarray-01 (previous step)

i ≤ j, 0 ≤ i, 0 ≤ j ⊦ putArray(vals, r, i, addarray(r, ty, j, st)) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + ((¬ j ≤ n→i(# vals) + i ⊃ mklist(initial_value(ty), i→n(j - i + n→i(# vals))); [])), st) [r -- _length, intval(j) ] )

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 118:
¬ j ≤ n→i(# vals) + i, i ≤ j, 0 ≤ i, 0 ≤ j ⊦ putArray(vals, r, i, addarray(r, ty, j, st)) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(j - i + n→i(# vals))), st)[r -- _length, intval(j)])
Proof step 227:
j ≤ n→i(# vals) + i, i ≤ j, 0 ≤ i, 0 ≤ j ⊦ putArray(vals, r, i, addarray(r, ty, j, st)) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + [], st)[r -- _length, intval(j)])

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]