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Proof step 31 from proof putByteArray-vals-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ¬ n < # vals → (vals + vals0)[n] = vals0[n - # vals]
Proof step 30:
¬ i→n(i0) < # mkjavavalues(bytes), 0 < n→i(# bytes) + i1, i0 < n→i(# bytes) + i1, 0 ≤ i1, 0 ≤ j, 0 ≤ n→i(# bytes) + i1, 0 ≤ j + n→i(# bytes) + i1, 0 < n→i(# bytes) + j, i0 < n→i(# bytes), 0 ≤ i0 + j, 0 ≤ i0 ⊦ bytes = [], (mkjavavalues(bytes)[i→n(i0)]) = (mklist(initial_value(byte_type), i→n(i1))[i→n(i0) - # mkjavavalues(bytes)])

Rule argument

[speclemmaarg: ,¬ n < # vals → (vals + vals0)[n] = vals0[n - # vals] ,[n, vals0, vals] → [i→n(i0), mklist(initial_value(byte_type), i→n(i1)), mkjavavalues(bytes)] ,F ,list-del ,javavalues ,get-append-grt ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n < # vals → (vals + vals0)[n] = vals[n]], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1])], [EXTRATERMS : (i→n(i0), mklist(initial_value(byte_type), i→n(i1)), mkjavavalues(bytes))]]