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Proof step 53 from proof addarray-put-01 (previous step)

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 '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
r -- sk ∈ addarray(r, ty, i0 + j + 1, st), is_indexkey(sk), 0 ≤ i0 + j, 0 ≤ i0, 0 < j ⊦ sk = _length, sk = _type, sk = j ', j = 0, r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)])]]