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Proof step 76 from proof putByteArray-vals-addarray-01 (previous step)

0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1 ⊦ (putArray(mkjavavalues(bytes), r, j, 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 21:
⊦ i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i ']
Proof step 42:
¬ (i < j ∨ n→i(# mkjavavalues(bytes)) + j ≤ i), 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1 ⊦ (putArray(mkjavavalues(bytes), r, j, 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 75:
i < j ∨ n→i(# mkjavavalues(bytes)) + j ≤ i, 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 ≤ i1 ⊦ (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 '])

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, putArray (mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)), r, 0, st), j, r, mkjavavalues(bytes)] ,F ,storearrays , ,putar-atother ]

Additional information

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