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Proof step 48 from proof getbytearray-pseq-02 (previous step)

st[r -- _length] .intval = i2 + i, 0 ≤ i, 0 < i2 + i, validref(`docs2store', r, mkarraytype(byte_type), st), 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) → ( validref(`docs2store', r0, mkarraytype(byte_type), st0) ∧ 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) ⊦ r = jvmref, st[r -- i '] .byteval ' + getbytearray(r, i + 1, i3, st) = st1[r1 -- i '] .byteval ' + getbytearray(r1, i + 1, i3, st1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ bytes ≠ [] → (by ' + bytes0 = bytes + bytes1 ↔ by = bytes .first ∧ bytes0 = bytes .rest + bytes1)
Proof step 47:
st1[r1 -- i '] .byteval ' ≠ [], st[r -- _length] .intval = i2 + i, 0 ≤ i, 0 < i2 + i, validref(`docs2store', r, mkarraytype(byte_type), st), 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) → ( validref(`docs2store', r0, mkarraytype(byte_type), st0) ∧ 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) ⊦ r = jvmref, st[r -- i '] .byteval = st1[r1 -- i '] .byteval ' .first ∧ getbytearray(r, i + 1, i3, st) = st1[r1 -- i '] .byteval ' .rest + getbytearray(r1, i + 1, i3, st1)

Rule argument

[speclemmaarg: , bytes ≠ [] → ( by ' + bytes0 = bytes + bytes1 ↔ by = bytes .first ∧ bytes0 = bytes .rest + bytes1) ,[bytes1, bytes, bytes0, by] → [getbytearray(r1, i + 1, i3, st1), st1[r1 -- i '] .byteval ', getbytearray(r, i + 1, i3, st), st[r -- i '] .byteval] ,F ,list ,bytelist ,c-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ by ' ≠ []])], [EXTRATERMS : (getbytearray(r1, i + 1, i3, st1), st1[r1 -- i '] .byteval ', getbytearray(r, i + 1, i3, st), st[r -- i '] .byteval)]]