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Proof step 19 from proof addclass-okarray (previous step)

st[r -- _length] = intval(i), _length ∈ fis, is_arrayref(r, i, st) ⊦ okreftype(refval(r), mkarraytype(ty), addclass(class, fis, st)) ∧ r -- _length ∈ addclass(class, fis, st) ∧ 0 ≤ i ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r -- _length ∈ st ∧ ¬ i < 0 ∧ (∀ j. 0 ≤ j ∧ j < i → okval(st[r -- j '], ty)), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 18:
st[r -- _length] = intval(i), _length ∈ fis, is_arrayref(r, i, st) ⊦ is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ addclass(class, fis, st) ∧ is_typevalue(addclass(class, fis, st)[refval(r) .refval -- _type]) ∧ (addclass(class, fis, st)[refval(r) .refval -- _type]) .type ≤ mkarraytype(ty)) ∧ r -- _length ∈ addclass(class, fis, st) ∧ 0 ≤ i ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r -- _length ∈ st ∧ ¬ i < 0 ∧ (∀ j. 0 ≤ j ∧ j < i → okval(st[r -- j '], ty)), r = jvmref

Rule argument

[speclemmaarg: , okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ ( val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty) ,[st, ty, val] → [addclass(class, fis, st), mkarraytype(ty), refval(r)] ,F ,okfuns , ,okreftype ]

Additional information

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