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Proof step 98 from proof putByteArray-vals-addarray-01 (previous step)

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) ] ) = (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 -- _length, intval(j + n→i(# bytes) + i1) ] )

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j)
Proof step 97:
0 ≤ j ∧ 0 ≤ n→i(# bytes) + i1, 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) + i→n(n→i(# bytes) + i1)), r, 0, st)) [r -- _type, typeval(mkarraytype(byte_type)) ] [r -- _length, intval(j + n→i(# bytes) + i1) ] ) = (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 -- _length, intval(j + n→i(# bytes) + i1) ] )

Rule argument

[speclemmaarg: 0 ≤ i, 0 ≤ j ,i→n(i + j) = i→n(i) + i→n(j) ,[j, i] → [n→i(# bytes) + i1, j] ,F ,intnat , ,add-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (n→i(# bytes) + i1, j)]]