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Proof step 35 from proof putByteArray-vals-addarray-01 (previous step)

0 ≤ i0, 0 ≤ i0 + j, i0 < n→i(# bytes), 0 < n→i(# bytes) + j, 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1, i0 < n→i(# bytes) + i1, 0 < n→i(# bytes) + i1 ⊦ bytes = [], (mkjavavalues(bytes)[i→n(i0)]) = (mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)))[i→n(i0 + j)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j)
Proof step 34:
0 ≤ i0 ∧ 0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j, i0 < n→i(# bytes), 0 < n→i(# bytes) + j, 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1, i0 < n→i(# bytes) + i1, 0 < n→i(# bytes) + i1 ⊦ bytes = [], (mkjavavalues(bytes)[i→n(i0)]) = (mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)))[i→n(i0) + i→n(j)]

Rule argument

[speclemmaarg: 0 ≤ i, 0 ≤ j ,i→n(i + j) = i→n(i) + i→n(j) ,[j, i] → [j, i0] ,F ,intnat , ,add-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (j, i0)]]