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Proof step 71 from proof addarray-put-01 (previous step)

j = 0, i ≤ n→i(# []) + i0, 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), 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
⊦ r ∈ addarray(r, ty0, vals, st)
Proof step 70:
0 < i0, 0 < i, r -- i ' ∈ addarray(r, ty, val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ i0, i ≤ i0 ⊦ i = 0, r -- i ' ∈ addarray(r, ty, 1 + i0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ [] + vals = vals], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ # [] = 0])]]