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Proof step 114 from proof putByteArray-vals-addarray-01 (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_fskey(sk) ∨ r ≠ r0 → addarray(r, val, i, st[r0 -- sk, val0]) = (addarray(r, val, i, st)[r0 -- sk, val0])
Proof step 113:
is_fskey(_length) ∨ r ≠ r, 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: add-put-switch , F , [val0, sk, r0, st, i, val, r] → [intval(j + n→i(# bytes) + i1), _length, r, st[r -- _type, typeval(mkarraytype(byte_type))], j + n→i(# bytes) + i1, initial_value(byte_type), r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(_length)])], [EXTRATERMS : (intval(j + n→i(# bytes) + i1), _length, r, st[r -- _type, typeval(mkarraytype(byte_type))], j + n→i(# bytes) + i1, initial_value(byte_type), r)]]