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Proof step 100 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, mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), 0, st) [r -- _type, typeval(mkarraytype(byte_type)) ] [r -- _length, intval(j + n→i(# bytes) + i1) ] )

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 0 ≤ i → addarray(r, val, i, st) = putArray(mklist(val, i→n(i)), r, 0, st)
Proof step 99:
0 ≤ j + n→i(# bytes) + i1, 0 ≤ i1, 0 ≤ j, 0 ≤ n→i(# bytes) + i1 ⊦ (putArray(mkjavavalues(bytes), r, j, putArray(mklist(initial_value(byte_type), i→n(j + n→i(# bytes) + i1)), r, 0, st)) [r -- _type, typeval(mkarraytype(byte_type)) ] [r -- _length, intval(j + n→i(# bytes) + i1) ] ) = (addarray(r, mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), 0, st) [r -- _type, typeval(mkarraytype(byte_type)) ] [r -- _length, intval(j + n→i(# bytes) + i1) ] )

Rule argument

[crewrite-arg: addarray-is-putarray , F , [st, i, val, r] → [st, j + n→i(# bytes) + i1, initial_value(byte_type), r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])], [EXTRATERMS : (st, j + n→i(# bytes) + i1, initial_value(byte_type), r)]]