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Proof step 10 from proof addarray-lastrec (previous step)

vals = vals0 + val ', i + n→i(# vals) = i0 + 1 ⊦ vals = [], addarray(r, vals, i, st) = (addarray(r, vals0, i, st)[r -- i0 ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ addarray(r, vals0 + val ', i, st) = (addarray(r, vals0, i, st)[r -- (n→i(# vals0) + i) ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ vals + val ' ≠ []], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ 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 : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0])]]