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Proof step 48 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→n(i1) + # bytes) + i→n(j) ≤ i→n(i), 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 47:
0 ≤ i ⊦ ((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i

Rule argument

[speclemmaarg: 0 ≤ i ,((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i ,[i, m] → [i, (i→n(i1) + # bytes) + i→n(j)] ,F ,intnat , ,num-i2n-le-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i, (i→n(i1) + # bytes) + i→n(j))]]