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Proof step 10 from proof is_array-norefval (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), type∃(str, ty), r -- _type ∈ st, okreftype(refval(r), mkarraytype(ty), 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 '], ty, st)), 0 ≤ i, 0 < st[r -- _length] .intval, r ∈ st, is_reftype(ty), i < st[r -- _length] .intval ⊦ r = jvmref, ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, is_referencevalue(st[r -- i '])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ 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 6:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 9:
st[r -- _type] = typeval(mkarraytype(ty)), 0 ≤ st[r -- _length] .intval, r -- _type ∈ st, type∃(str, ty), i < st[r -- _length] .intval, is_reftype(ty), r ∈ st, 0 < st[r -- _length] .intval, 0 ≤ i, is_arrayref(r, st[r -- _length] .intval, st), is_integervalue(st[r -- _length]), r -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_referencevalue(st[r -- j ']) ⊦ r = jvmref, ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, is_referencevalue(st[r -- i '])

Rule argument

[emptyarg]

Additional information

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