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Proof step 80 from proof putByteArray-vals-addarray-01 (previous step)

0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1 ⊦ sk = _length, sk = _type, (putArray(mkjavavalues(bytes), r, j, putArray(mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)), r, 0, st))[r -- sk]) = (putArray(mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), r, 0, st)[r -- sk])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ is_fskey(sk) → (putArray(vals, r, i, st)[r -- sk]) = st[r -- sk]
Proof step 79:
¬ is_fskey(sk), 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1 ⊦ sk = _length, sk = _type, (putArray(mkjavavalues(bytes), r, j, putArray(mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)), r, 0, st))[r -- sk]) = (putArray(mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), r, 0, st)[r -- sk])

Rule argument

[speclemmaarg: ,is_fskey(sk) → (putArray(vals, r, i, st)[r -- sk]) = st[r -- sk] ,[sk, st, i, r, vals] → [sk, putArray (mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)), r, 0, st), j, r, mkjavavalues(bytes)] ,F ,storearrays , ,putArray-at ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(sk) → (putArray(vals, r, i, st) [r0 -- sk ] ) = st[r0 -- sk]])], [EXTRATERMS : (sk, putArray (mklist (initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)), r, 0, st), j, r, mkjavavalues(bytes))]]