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Proof step 33 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 ⊦ (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)], bytes = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 32:
¬ i→n(i0) + i→n(j) < # mklist(initial_value(byte_type), i→n(j)), 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 ⊦ (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)], bytes = []

Rule argument

[speclemmaarg: ,n < # vals → (vals + vals0)[n] = vals[n] ,[n, vals0, vals] → [i→n(i0) + i→n(j), 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 : ([CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ ¬ m + n < m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (i→n(i0) + i→n(j), mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), mklist(initial_value(byte_type), i→n(j)))]]