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Proof step 3 from proof move-initvals-02 (previous step)

⊦ addarray(r, ty, (val ' + val0 ' + vals)[1, val1], st) = addarray(r, ty, val ' + val1 ' + vals, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ n ≠ 0 ∧ vals ≠ [] → vals[n, val] = vals .first ' + (vals .rest)[n -1, val]

Rule argument

[speclemmaarg: , n ≠ 0 ∧ vals ≠ [] → vals[n, val] = vals .first ' + (vals .rest)[n -1, val] ,[val, n, vals] → [val1, 1, val ' + val0 ' + vals] ,F ,list-del ,javavalues ,put-rec ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ val ' ≠ []], [CSIMPSEQ : ⊦ ¬ vals + vals0 ≠ [] ↔ vals = [] ∧ vals0 = []], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ (val ' + vals) .first = val], [CSIMPSEQ : ⊦ (val ' + vals) .rest = vals], [CSIMPSEQ : ⊦ (val ' + vals)[0, val0] = val0 + vals], [CSIMPSEQ : ⊦ val + vals = val ' + vals], [CSIMPSEQ : ⊦ val ' + vals ≠ []])], [EXTRATERMS : (val1, 1, val ' + val0 ' + vals)]]