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Proof step 18 from proof addclass-okarray (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
r ≠ jvmref ⊦ (addclass(class1, fis, st)[r -- sk]) = st[r -- sk]
Proof step 17:
st[r -- _length] = intval(i), _length ∈ fis, is_arrayref(r, i, st) ⊦ r = jvmref, r -- _type ∈ addclass(class, fis, st) ∧ is_typevalue(st[r -- _type]) ∧ is_arraytype(st[r -- _type] .type) ∧ st[r -- _type] .type .type ≤ 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))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]