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Proof step 74 from proof putByteArray-vals-addarray-01 (previous step)

0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1, 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 43:
⊦ i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i ']
Proof step 70:
¬ (i < 0 ∨ n→i(# mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j))) + 0 ≤ i), 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1, 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 '])
Proof step 73:
i < 0 ∨ n→i(# mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j))) + 0 ≤ i, 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1, i < j ∨ n→i(# bytes) + j ≤ i ⊦ 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 '])

Rule argument

[speclemmaarg: , i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i '] ,[i, r0, st, j, r, vals] → [i, r, st, 0, r, mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j))] ,F ,storearrays , ,putar-atother ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i, r, st, 0, r, mklist (initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)))]]