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Proof step 10 from proof exactarray-putin (previous step)

exactreftype(refval(r), mkarraytype(mkclasstype(class)), st) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(st[r -- _length] .intval) ∈ st ∧ is_arrayref(refval(r) .refval, st[r -- _length] .intval, st) ⊦ r = jvmref, exactreftype(refval(r), mkarraytype(mkclasstype(class)), st[r -- i ', refval(r0)]) ∧ r -- _length ∈ st ∧ st[r -- _length] = intval(st[r -- _length] .intval) ∧ is_arrayref(r, st[r -- _length] .intval, st[r -- i ', refval(r0)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ 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 9:
st[r -- _type] .type = mkarraytype(mkclasstype(class)), st[r -- _length] = intval(st[r -- _length] .intval), r -- _type ∈ st, is_typevalue(st[r -- _type]), r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), r ∈ st ⊦ r = jvmref, exactreftype(refval(r), mkarraytype(mkclasstype(class)), st[r -- i ', refval(r0)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ is_arrayref(r, i, st) → is_arrayref (r, i, st[r -- j ', val])], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]