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Proof step 88 from proof addarray-put-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 87:
0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j, r -- i ' ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st), i ≤ n→i(# ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j))))) + i0, 0 ≤ n→i(# ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j))))) + i0, 0 ≤ i ⊦ i = j, r -- i ' ∈ addarray(r, ty, i0 + j + 1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ is_indexkey(i ')], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ _type ≠ i '], [CSIMPSEQ : ⊦ _length ≠ i '])]]