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Proof step 82 from proof putByteArray-vals-addarray-01 (previous step)

0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1 ⊦ (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 weak cut applied rule cut formula

And obtained the following new goals

Proof step 81:
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

Rule argument

[fma-arg: r -- sk = r -- _type]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ _type ≠ _length], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ typeval(ty) = typeval(ty0) ↔ ty = ty0])], [EXTRAFMAS : (r -- sk = r -- _type)]]