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Proof step 94 from proof addarray-put-01 (previous step)

0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j, is_indexkey(sk) ⊦ sk = j ', r -- sk ∈ 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), sk = _type, sk = _length

User applied rule case distinction

And obtained the following new goals

Proof step 57:
r -- sk ∈ addarray(r, ty, i0 + j + 1, st), 0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j, is_indexkey(sk) ⊦ r -- sk ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st), sk = j ', sk = _type, sk = _length
Proof step 93:
r -- sk ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j, is_indexkey(sk) ⊦ r -- sk ∈ addarray(r, ty, i0 + j + 1, st), sk = j ', sk = _type, sk = _length

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]