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Proof step 9 from proof addarray-mklist-03 (previous step)

mklist(val, m0) + val ' ≠ [], 0 ≤ n→i(m) + n→i(m0), ∀ r, val, m, st. addarray(r, mklist(val, m0), n→i(m), addarray(r, mklist(val, m), 0, st)) = addarray(r, val, n→i(m0) + n→i(m), st) ⊦ (addarray(r, (mklist(val, m0) + val ') .butlast, n→i(m), addarray(r, mklist(val, m), 0, st)) [r -- (n→i(m) + n→i(# (mklist(val, m0) + val ')) - 1) ', (mklist(val, m0) + val ') .last ] ) = (addarray(r, val, n→i(m0) + n→i(m), st)[r -- (n→i(m0) + n→i(m)) ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 ≤ n→i(m) + n→i(m0), ∀ r, val, m, st. addarray(r, mklist(val, m0), n→i(m), addarray(r, mklist(val, m), 0, st)) = addarray(r, val, n→i(m0) + n→i(m), st) ⊦ (addarray(r, mklist(val, m0), n→i(m), addarray(r, mklist(val, m), 0, st))[r -- (n→i(m) + n→i(m0)) ', val]) = (addarray(r, val, n→i(m0) + n→i(m), st)[r -- (n→i(m0) + n→i(m)) ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ vals + val ' ≠ []], [CSIMPSEQ : ⊦ (vals + val ') .last = val], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ (vals + val ') .butlast = vals])]]