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Proof step 33 from proof getbytearray-pseq-nojunk-02 (previous step)

st[r -- _type] .type = mkarraytype(byte_type), st[r -- _length] .intval = i2 + i, 0 ≤ i, 0 < i2 + i, ps=(r, st, r1, st1), i3 < i2, 0 < i2, 0 ≤ i2, 0 ≤ i3, ∀ i1, st1, r1, i0, r0, st0. i→n(st0[r0 -- _length] .intval - i0) < i→n(i2) → ( st0[r0 -- _type] .type = mkarraytype(byte_type) ∧ ps=(r0, st0, r1, st1) ∧ i0 < st0[r0 -- _length] .intval ∧ i0 + i1 ≤ st0[r0 -- _length] .intval ∧ 0 ≤ i0 ∧ 0 < st0[r0 -- _length] .intval ∧ 0 ≤ i1 → getbytearray(r0, i0, i1, st0) = getbytearray(r1, i0, i1, st1) ∨ r0 = jvmref ∨ junkref(`docs2store', r0, st0)) ⊦ r = jvmref, st[r -- i '] .byteval ' + getbytearray(r, i + 1, i3, st) = getbytearray(r1, i, i3 + 1, st1), junkref(`docs2store', r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 < j → getbytearray(r, i, j, st) = st[r -- i '] .byteval + getbytearray(r, i + 1, j - 1, st)
Proof step 32:
0 < i3 + 1, st[r -- _type] .type = mkarraytype(byte_type), st[r -- _length] .intval = i2 + i, 0 ≤ i, 0 < i2 + i, ps=(r, st, r1, st1), i3 < i2, 0 < i2, 0 ≤ i2, 0 ≤ i3, ∀ i1, st1, r1, i0, r0, st0. i→n(st0[r0 -- _length] .intval - i0) < i→n(i2) → ( st0[r0 -- _type] .type = mkarraytype(byte_type) ∧ ps=(r0, st0, r1, st1) ∧ i0 < st0[r0 -- _length] .intval ∧ i0 + i1 ≤ st0[r0 -- _length] .intval ∧ 0 ≤ i0 ∧ 0 < st0[r0 -- _length] .intval ∧ 0 ≤ i1 → getbytearray(r0, i0, i1, st0) = getbytearray(r1, i0, i1, st1) ∨ r0 = jvmref ∨ junkref(`docs2store', r0, st0)) ⊦ r = jvmref, st[r -- i '] .byteval ' + getbytearray(r, i + 1, i3, st) = st1[r1 -- i '] .byteval + getbytearray(r1, i + 1, i3 + 1 - 1, st1), junkref(`docs2store', r, st)

Rule argument

[speclemmaarg: , 0 < j → getbytearray(r, i, j, st) = st[r -- i '] .byteval + getbytearray(r, i + 1, j - 1, st) ,[st, j, i, r] → [st1, i3 + 1, i, r1] ,F ,storearrays , ,getbar-rec ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (st1, i3 + 1, i, r1)]]