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Proof step 64 from proof putByteArray-vals-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 60:
¬ i→n(i) < # mklist(initial_value(byte_type), i→n(j)), i→n(i) < (i→n(i1) + # bytes) + i→n(j), 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1, 0 ≤ i, 0 < n→i(# bytes) + i1 + j, i < n→i(# bytes) + i1 + j, i < n→i(# bytes) + j + i1, i < j ∨ n→i(# bytes) + j ≤ i ⊦ initial_value(byte_type) = (mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)))[i→n(i)]
Proof step 63:
i→n(i) < # mklist(initial_value(byte_type), i→n(j)), i→n(i) < (i→n(i1) + # bytes) + i→n(j), 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1, 0 ≤ i, 0 < n→i(# bytes) + i1 + j, i < n→i(# bytes) + i1 + j, i < n→i(# bytes) + j + i1, i < j ∨ n→i(# bytes) + j ≤ i ⊦ initial_value(byte_type) = (mklist(initial_value(byte_type), i→n(j))[i→n(i)])

Rule argument

[speclemmaarg: ,n < # vals → (vals + vals0)[n] = vals[n] ,[n, vals0, vals] → [i→n(i), mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), mklist(initial_value(byte_type), i→n(j))] ,F ,list-del ,javavalues ,get-append-less ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i→n(i), mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), mklist(initial_value(byte_type), i→n(j)))]]