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Proof step 15 from proof okbytearray-put-byteval-equiv (previous step)

st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(byte_type)), r -- _type ∈ st, r -- _length ∈ st, r ∈ st, 0 ≤ i0, i < i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r -- i ', byteval(by)][r -- j ']), 0 ≤ i ∧ r -- i ' ∈ st ∧ is_bytevalue(st[r -- i ']) ∨ i < 0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → r -- j ' ∈ st[r -- i ', byteval(by)] ⊦ r = jvmref, is_arrayref(r, i0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 14:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(byte_type)), r -- _type ∈ st, r -- _length ∈ st, r ∈ st, 0 ≤ i0, i < i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r -- i ', byteval(by)][r -- j ']), 0 ≤ i ∧ r -- i ' ∈ st ∧ is_bytevalue(st[r -- i ']) ∨ i < 0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → r -- j ' ∈ st[r -- i ', byteval(by)] ⊦ r = jvmref, ∀ j. 0 ≤ j ∧ j < i0 → r -- j ' ∈ st

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [st, i0, r] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i0, r)]]