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Proof step 24 from proof move-initvals (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
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))) ⊦ (addarray(r, ty, vals1, st)[r -- n→i(# vals1) ', val0][r -- _length, intval(n→i(# vals1) + 1)][r -- i ', val]) = addarray(r, ty, (vals1 + val0 ')[i→n(i), val], st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ vals + val ' ≠ []], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0])]]