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Proof step 24 from proof putarray-add-butlast (previous step)

⊦ putArray(vals, r, 0, addarray(r, ty, n→i(# vals) + 1, st)) = addarray(r, ty, vals + initial_value(ty) ', st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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))])
Proof step 23:
vals + initial_value(ty) ' ≠ [] ⊦ putArray(vals, r, 0, addarray(r, ty, n→i(# vals) + 1, st)) = (addarray(r, ty, (vals + initial_value(ty) ') .butlast, st)[r -- n→i((# (vals + initial_value(ty) ')) -1) ', (vals + initial_value(ty) ') .last] [r -- _length, intval(n→i(# (vals + initial_value(ty) '))) ] )

Rule argument

[crewrite-arg: add-lastrec , F , [st, vals, ty, r] → [st, vals + initial_value(ty) ', ty, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ vals + vals0 ≠ [] ↔ vals = [] ∧ vals0 = []], [CSIMPSEQ : ⊦ val ' ≠ []], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1])], [EXTRATERMS : (st, vals + initial_value(ty) ', ty, r)]]