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Proof step 81 from proof putByteArray-vals-addarray-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]