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Proof step 6 from proof move-initvals (previous step)

∀ 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) ', val][r -- _length, intval(n→i(# vals1) + 1)]) = addarray(r, ty, vals1 + val ', st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ vals ≠ [] → addarray(r, ty, vals, st) = (addarray(r, ty, vals .butlast, st)[r -- n→i((# vals) -1) ', vals .last][r -- _length, intval(n→i(# vals))])

Rule argument

[crewrite-arg: add-lastrec , F , [st, vals, ty, r] → [st, vals1 + val ', ty, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ val ' ≠ []], [CSIMPSEQ : ⊦ ¬ vals + vals0 ≠ [] ↔ vals = [] ∧ vals0 = []], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ (vals + val ') .butlast = vals], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ (m + 1) -1 = m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (vals + val ') .last = val], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ vals + val ' ≠ []])], [EXTRATERMS : (st, vals1 + val ', ty, r)]]