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Proof step 12 from proof getarray-addarray-03 (previous step)

1 < i1 + 1, 0 ≤ i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i1 + 1 - 1, addarray(r, val, i1, st)[r -- i1 ', val]) + (addarray(r, val, i1, st)[r -- i1 ', val][r -- (0 + i1 + 1 - 1) ']) = mklist(val, i→n(i1)) + val '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 ≤ i1, 0 < i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i1, addarray(r, val, i1, st)[r -- i1 ', val]) = mklist(val, i→n(i1))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ vals + vals0 = vals1 + vals0 ↔ vals = vals1], [CSIMPSEQ : ⊦ vals + val = vals + val '], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0])]]