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Proof step 17 from proof putarray-add-butlast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i = n→i(# vals) ∧ val = initial_value(ty) → putArray(vals, r, 0, addarray(r, val, i, st)) = addarray(r, vals, 0, st)
Proof step 16:
n→i(# vals) = n→i(# vals) ∧ initial_value(ty) = initial_value(ty) ⊦ (addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals) + 1)])[r -- n→i(# vals) ', initial_value(ty)]) = (addarray(r, ty, vals, st)[r -- n→i(# vals) ', initial_value(ty)][r -- _length, intval(n→i(# vals) + 1)])

Rule argument

[crewrite-arg: putarray-add-same-02 , F , [i, vals, val, ty, r, st] → [n→i(# vals), vals, initial_value(ty), ty, r, st[r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(n→i(# vals) + 1) ]] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (n→i(# vals), vals, initial_value(ty), ty, r, st[r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(n→i(# vals) + 1) ])]]