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Proof step 69 from proof putByteArray-vals-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ j ≤ i ∧ i < n→i(# vals) + j → (putArray(vals, r, j, st)[r -- i ']) = vals[i→n(i - j)]
Proof step 68:
0 ≤ i ∧ i < n→i(# mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j))) + 0, 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1, i < n→i(# bytes) + i1 + j, 0 ≤ i, 0 < n→i(# bytes) + i1 + j, i < j ∨ n→i(# bytes) + j ≤ i ⊦ (mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j))[i→n(i - 0)]) = (putArray(mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), r, 0, st)[r -- i '])

Rule argument

[speclemmaarg: , j ≤ i ∧ i < n→i(# vals) + j → (putArray(vals, r, j, st)[r -- i ']) = vals[i→n(i - j)] ,[i, st, j, r, vals] → [i, st, 0, r, mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j))] ,F ,storearrays , ,putar-at ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [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 + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i, st, 0, r, mklist (initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)))]]