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Proof step 26 from proof okarray-08 (previous step)

is_integervalue(val), okreftype(refval(r0), mkarraytype(int_type), st) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → oktype(st[r0 -- j '], int_type, st)), r0 ∈ st ⊦ r0 = jvmref, okreftype(refval(r0), mkarraytype(int_type), st[r0 -- j ', val]) ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ is_arrayref(r0, st[r0 -- _length] .intval, st[r0 -- j ', val]) ∧ (0 ≤ j0 ∧ j0 < st[r0 -- _length] .intval → is_integervalue(st[r0 -- j ', val][r0 -- j0 ']))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ 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 9:
⊦ oktype(val, int_type, st) ↔ is_integervalue(val)
Proof step 25:
st[r0 -- _type] .type .type = int_type, r0 -- _length ∈ st, is_integervalue(st[r0 -- _length]), is_arrayref(r0, st[r0 -- _length] .intval, st), is_integervalue(val), r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), is_arraytype(st[r0 -- _type] .type), 0 ≤ st[r0 -- _length] .intval, r0 ∈ st, ∀ j1. ¬ j1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j1 → is_integervalue(st[r0 -- j1 ']) ⊦ r0 = jvmref, okreftype(refval(r0), mkarraytype(int_type), st[r0 -- j ', val]) ∧ (0 ≤ j0 ∧ j0 < st[r0 -- _length] .intval → is_integervalue(st[r0 -- j ', val][r0 -- j0 ']))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ is_arrayref(r, i, st) → is_arrayref (r, i, st[r -- j ', val])], [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))])]]