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Proof step 25 from proof move-initvals (previous step)

# 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, vals .butlast, st)[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(m) + 1)][r -- i ', val]) = addarray(r, ty, vals[i→n(i), val], st), vals = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
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 = []

Rule argument

[speclemmaarg: vals ≠ [] ,val = vals .last ∧ vals0 = vals .butlast ↔ vals = vals0 + val ' ,[vals, val, vals0] → [vals, val0, vals1] ,T ,list-last ,javavalues ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : vals ≠ [] ⊦ val = vals .last ∧ vals0 = vals .butlast ↔ vals = vals0 + val '])], [EXTRATERMS : (vals, val0, vals1)]]