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Proof step 24 from proof okarray-copy (previous step)

st[r0 -- _length] = intval(i), 0 ≤ i, r0 ∈ st, is_arrayref(r0, i, st), r0 -- _length ∈ st, okreftype(refval(r0), mkarraytype(byte_type), st), ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → is_bytevalue(st[r0 -- j0 ']) ⊦ r0 = jvmref, r = jvmref, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st)) ∧ is_typevalue(arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))[refval(r) .refval -- _type]) ∧ (arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))[refval(r) .refval -- _type]) .type ≤ mkarraytype(byte_type)) ∧ is_arrayref(r, i, arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))) ∧ (0 ≤ j ∧ j < i → is_bytevalue(arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))[r -- j ']))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ r -- _type ∈ addarray(r, ty, i, st)
Proof step 7:
⊦ (addarray(r, ty, i, st)[r -- _type]) = typeval(mkarraytype(ty))
Proof step 23:
st[r0 -- _length] = intval(i), 0 ≤ i, r0 ∈ st, is_arrayref(r0, i, st), r0 -- _length ∈ st, okreftype(refval(r0), mkarraytype(byte_type), st), ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → is_bytevalue(st[r0 -- j0 ']) ⊦ r0 = jvmref, r = jvmref, is_arrayref(r, i, arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))) ∧ (0 ≤ j ∧ j < i → is_bytevalue(arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))[r -- j ']))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ byte_type ≤ ty ↔ ty = byte_type], [CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ (arraycopy(r1, i1, r2, i2, j, st) [r -- _type ] ) = st[r -- _type]], [CSIMPSEQ : ⊦ r -- _type ∈ arraycopy (r1, i1, r2, i2, j, st) ↔ r -- _type ∈ st], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]