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Proof step 21 from proof add-lastrec (previous step)

# vals = m + 1 ⊦ vals = [], addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m) + 1)]) = (addarray(r, vals .butlast, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m))])[r -- n→i(m) ', vals .last] [r -- _length, intval(n→i(m) + 1) ] )

User applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
vals = vals0 + val ', # vals = m + 1 ⊦ vals = [], addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m) + 1)]) = (addarray(r, vals0, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m))])[r -- n→i(m) ', val][r -- _length, intval(n→i(m) + 1)] )

Rule argument

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

Additional information

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