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Proof step 57 from proof putByteArray-vals-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
0 ≤ i ⊦ i→n(i) = ((* m)) ↔ i = n→i(m)
Proof step 56:
0 ≤ i, i = n→i(n + i→n(j)), n < i→n(i1) + # bytes, n→i(# bytes) + j ≤ i, i < n→i(# bytes) + j + i1, i < n→i(# bytes) + i1 + j, 0 < n→i(# bytes) + i1 + j, 0 ≤ i, 0 ≤ i1, 0 ≤ j, 0 ≤ n→i(# bytes) + i1, 0 ≤ j + n→i(# bytes) + i1, i→n(i) < (i→n(i1) + # bytes) + i→n(j), 0 < i1, 0 < n→i(# bytes) + i1, j ≤ i ⊦ initial_value(byte_type) = (mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)))[n]

Rule argument

[speclemmaarg: 0 ≤ i ,i→n(i) = ((* m)) ↔ i = n→i(m) ,[m, i] → [n + i→n(j), i] ,F ,intnat , ,num-i2n-eq ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (n + i→n(j), i)]]