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Proof step 16 from proof move-initvals (previous step)

vals1[i→n(i), val] + val0 ' ≠ [], 0 ≤ i, i→n(i) < # vals1, ∀ val, st, ty, r, i, vals0. # vals0 < # vals1 + 1 → (true → (0 ≤ i ∧ i→n(i) < # vals0 → (addarray(r, ty, vals0, st)[r -- i ', val]) = addarray(r, ty, vals0[i→n(i), val], st))) ⊦ i = n→i(# vals1), (addarray(r, ty, vals1, st)[r -- i ', val][r -- n→i(# vals1) ', val0][r -- _length, intval(n→i(# vals1) + 1)]) = (addarray(r, ty, (vals1[i→n(i), val] + val0 ') .butlast, st)[r -- n→i((# (vals1[i→n(i), val] + val0 ')) -1) ', (vals1[i→n(i), val] + val0 ') .last] [r -- _length, intval(n→i(# (vals1[i→n(i), val] + val0 '))) ] ), vals1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
0 ≤ i, i→n(i) < # vals1, ∀ val, st, ty, r, i, vals0. # vals0 < # vals1 + 1 → (true → (0 ≤ i ∧ i→n(i) < # vals0 → (addarray(r, ty, vals0, st)[r -- i ', val]) = addarray(r, ty, vals0[i→n(i), val], st))) ⊦ vals1 = [], i = n→i(# vals1), (addarray(r, ty, vals1, st)[r -- i ', val][r -- n→i(# vals1) ', val0][r -- _length, intval(n→i(# vals1) + 1)]) = (addarray(r, ty, vals1[i→n(i), val], st)[r -- n→i(# vals1) ', val0][r -- _length, intval(n→i(# vals1) + 1)])

Rule argument

[emptyarg]

Additional information

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