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Proof step 9 from proof isarray-abstract (previous step)

st[r -- _type] = typeval(mkarraytype(abstract_type)), r -- _type ∈ st, okreftype(refval(r), mkarraytype(abstract_type), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], abstract_type, st)), r ∈ st ⊦ st[r -- _length] .intval = 0, r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ 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 5:
⊦ ¬ oktype(val, abstract_type, st)
Proof step 8:
st[r -- _type] = typeval(mkarraytype(abstract_type)), 0 < st[r -- _length] .intval, is_integervalue(st[r -- _length]), r -- _length ∈ st, r -- _type ∈ st, r ∈ st, is_arrayref(r, st[r -- _length] .intval, st), ∀ j. j < 0 ∨ st[r -- _length] .intval ≤ j ⊦ r = jvmref, st[r -- _length] .intval = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ ty ≤ abstract_type ↔ ty = abstract_type], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]