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Proof step 131 from proof addarray-put-01 (previous step)

¬ i→n(i) < # val ', 0 ≤ i0, i ≤ i0, 0 < i, 0 < i0 ⊦ (addarray(r, ty, 1 + i0, st)[r -- i ']) = (val ' + mklist(initial_value(ty), i→n(i0)))[i→n(i)], i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 130:
0 ≤ i0, i ≤ i0, 0 < i, 0 < i0 ⊦ i = 0, (addarray(r, ty, 1 + i0, st)[r -- i ']) = (mklist(initial_value(ty), i→n(i0))[i→n(i) - 1])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < 1 ↔ i ≤ 0], [CSIMPSEQ : 0 ≤ i ⊦ i→n(i) < ((* m)) ↔ i < n→i(m)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ ¬ n < # vals → (vals + vals0)[n] = vals0[n - # vals]])]]