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Proof step 65 from proof putByteArray-vals-addarray-01 (previous step)

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 ⊦ (mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j))[i→n(i)]) = (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 46:
⊦ m < n → (mklist(val, n)[m]) = val
Proof step 49:
¬ 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 ⊦ (mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j))[i→n(i)]) = (mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)))[i→n(i)]
Proof step 64:
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)]

Rule argument

[speclemmaarg: ,m < n → (mklist(val, n)[m]) = val ,[m, n, val] → [i→n(i), (i→n(i1) + # bytes) + i→n(j), initial_value(byte_type)] ,F ,list-del ,javavalues ,get-mklist-01 ]

Additional information

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