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Proof step 54 from proof addarray-put-01 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 42:
j = 0, is_indexkey(sk), 0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j, r -- sk ∈ addarray(r, ty, i0 + j + 1, st) ⊦ r -- sk ∈ addarray(r, ty, [] + val ' + mklist(initial_value(ty), i→n(i0)), st), sk = _length, sk = _type, sk = j '
Proof step 53:
j ≠ 0, is_indexkey(sk), 0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j, r -- sk ∈ 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), sk = _length, sk = _type, sk = j '

Rule argument

[CASEDARG : pos: right 4, ()]

Additional information

[[CONCRETESIMPRULES : ()]]