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Proof step 46 from proof okarray-putarray-addarray-put (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ n→i(# vals0), j ≤ n→i(# vals) + i, ∀ val. val ∈ vals ∨ val ∈ vals0 → is_bytevalue(val) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(byte_type), putArray(vals, r, i, addarray(r, byte_type, vals0, st))[r -- _length, intval(j)]) ∧ is_arrayref(r, j, putArray(vals, r, i, addarray(r, byte_type, vals0, st))) ∧ (0 ≤ j0 ∧ j0 < j → is_bytevalue(putArray(vals, r, i, addarray(r, byte_type, vals0, st))[r -- j0 ']))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 45:
0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ n→i(# vals0), j ≤ n→i(# vals) + i, ∀ val. val ∈ vals ∨ val ∈ vals0 → is_bytevalue(val) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(byte_type), putArray(vals, r, i, addarray(r, byte_type, vals0, st))[r -- _length, intval(j)]) ∧ (∀ j0. 0 ≤ j0 ∧ j0 < j → r -- j0 ' ∈ putArray(vals, r, i, addarray(r, byte_type, vals0, st))) ∧ (0 ≤ j0 ∧ j0 < j → is_bytevalue(putArray(vals, r, i, addarray(r, byte_type, vals0, st))[r -- j0 ']))

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [putArray(vals, r, i, addarray(r, byte_type, vals0, st)), j, r] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (putArray (vals, r, i, addarray(r, byte_type, vals0, st)), j, r)]]