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Proof step 115 from proof putByteArray-vals-addarray-01 (previous step)

0 ≤ i1, 0 ≤ j, 0 ≤ n→i(# bytes) + i1 ⊦ putArray(mkjavavalues(bytes), r, j, addarray(r, byte_type, j + n→i(# bytes) + i1, st)) = addarray(r, byte_type, mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ addarray(r, ty, i, st) = addarray(r, initial_value(ty), i, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)])
Proof step 114:
0 ≤ i1, 0 ≤ j, 0 ≤ n→i(# bytes) + i1 ⊦ putArray (mkjavavalues(bytes), r, j, addarray (r, initial_value(byte_type), j + n→i(# bytes) + i1, st[r -- _type, typeval(mkarraytype(byte_type))][r -- _length, intval(j + n→i(# bytes) + i1)])) = addarray(r, byte_type, mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), st)

Rule argument

[crewrite-arg: addarray-def , F , [st, i, ty, r] → [st, j + n→i(# bytes) + i1, byte_type, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, j + n→i(# bytes) + i1, byte_type, r)]]