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Proof step 12 from proof addclass-exactarray (previous step)

⊦ r = jvmref, exactreftype(refval(r), mkarraytype(ty), addclass(class0, fis, st)) ∧ r -- _length ∈ addclass(class0, fis, st) ∧ st[r -- _length] = intval(i) ∧ is_arrayref(r, i, st) ↔ exactreftype(refval(r), mkarraytype(ty), st) ∧ r -- _length ∈ st ∧ st[r -- _length] = intval(i) ∧ is_arrayref(r, i, st)

User applied rule insert rewrite lemma

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 11:
⊦ r = jvmref, is_referencevalue(refval(r)) ∧ refval(r) .refval ∈ addclass(class0, fis, st) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ addclass(class0, fis, st) ∧ is_typevalue(addclass(class0, fis, st)[refval(r) .refval -- _type]) ∧ (addclass(class0, fis, st)[refval(r) .refval -- _type]) .type = mkarraytype(ty)) ∧ r -- _length ∈ addclass(class0, fis, st) ∧ st[r -- _length] = intval(i) ∧ is_arrayref(r, i, st) ↔ exactreftype(refval(r), mkarraytype(ty), st) ∧ r -- _length ∈ st ∧ st[r -- _length] = intval(i) ∧ is_arrayref(r, i, st)

Rule argument

[speclemmaarg: , 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) ,[st, ty, val] → [addclass(class0, fis, st), mkarraytype(ty), refval(r)] ,F ,okfuns , ,exactreftype ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addclass(class0, fis, st), mkarraytype(ty), refval(r))]]