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Proof step 11 from proof exactarray-put-03 (previous step)

⊦ r = r0, exactreftype(refval(r), mkarraytype(byte_type), st[r0 -- sk, val0]) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i) ∈ st[r0 -- sk, val0] ∧ is_arrayref(refval(r) .refval, i, st[r0 -- sk, val0]) ↔ exactarray(refval(r), byte_type, i, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ exactreftype(val, ty, st) ↔ is_referencevalue(val) ∧ val .refval ∈ st ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = ty)
Proof step 10:
⊦ r = r0, r ∈ st ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ st[r -- _type] .type = mkarraytype(byte_type) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ st[r -- _length] = intval(i) ∧ is_arrayref(r, i, st) ↔ exactarray(refval(r), byte_type, i, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_arrayref (r, i, st[r0 -- sk, val0]) ↔ is_arrayref(r, i, st))], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ r ≠ r0 → ( r -- sk ∈ st[r0 -- sk0, val] ↔ r -- sk ∈ st)], [CSIMPSEQ : ⊦ r ∈ st[r0 -- sk, val] ↔ r = r0 ∨ r ∈ st], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]