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Proof step 13 from proof putByteArray-vals-addarray (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ is_fskey(sk) ∨ r0 ≠ r → putArray(vals, r, i, st[r0 -- sk, val]) = (putArray(vals, r, i, st)[r0 -- sk, val])
Proof step 12:
is_fskey(_type) ∨ r ≠ r, 0 ≤ j ⊦ (putArray(mkjavavalues(bytes), r, j, addarray(r, initial_value(byte_type), n→i(# bytes) + j, st))[r -- _type, typeval(mkarraytype(byte_type))] [r -- _length, intval(n→i(# bytes) + j) ] ) = (addarray(r, mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes), 0, st)[r -- _type, typeval(mkarraytype(byte_type))] [r -- _length, intval(j + n→i(# bytes)) ] )

Rule argument

[speclemmaarg: , is_fskey(sk) ∨ r0 ≠ r → putArray(vals, r, i, st[r0 -- sk, val]) = (putArray(vals, r, i, st)[r0 -- sk, val]) ,[val, sk, r0, st, i, r, vals] → [typeval(mkarraytype(byte_type)), _type, r, addarray(r, initial_value(byte_type), n→i(# bytes) + j, st), j, r, mkjavavalues(bytes)] ,F ,storearrays , ,putArray-put-switch-02 ]

Additional information

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