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Proof step 6 from proof intval-01 (previous step)

okreftype(refval(r), mkarraytype(int_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 '], int_type, st)), i < st[r -- _length] .intval, r ∈ st, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ r = jvmref, is_integervalue(st[r -- i '])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ 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 4:
⊦ oktype(val, int_type, st) ↔ is_integervalue(val)
Proof step 5:
st[r -- _type] .type .type = int_type, r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), 0 ≤ st[r -- _length] .intval, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_integervalue(st[r -- j ']) ⊦ r = jvmref, is_integervalue(st[r -- i '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty ≤ int_type ↔ ty = int_type], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]