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

⊦ r = jvmref, r ∈ st ∧ r -- _type ∈ addclass(class0, fis, st) ∧ is_typevalue(st[r -- _type]) ∧ st[r -- _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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 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:
⊦ rk ∈ st → rk ∈ addclass(class, fis, 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] → [st, mkarraytype(ty), refval(r)] ,F ,okfuns , ,exactreftype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ is_typevalue(noval)], [CSIMPSEQ : ⊦ intval(i) ≠ noval])], [EXTRATERMS : (st, mkarraytype(ty), refval(r))]]