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Proof step 20 from proof okarray-put-other (previous step)

⊦ r = r1, okreftype(refval(r), mkarraytype(ty), st[r1 -- sk, val]) ∧ r ≠ jvmref ∧ r -- _length ∈ st[r1 -- sk, val] ∧ is_integervalue(st[r1 -- sk, val][r -- _length]) ∧ 0 ≤ (st[r1 -- sk, val][r -- _length]) .intval ∧ is_arrayref(r, (st[r1 -- sk, val][r -- _length]) .intval, st[r1 -- sk, val]) ∧ (∀ j. 0 ≤ j ∧ j < (st[r1 -- sk, val][r -- _length]) .intval → oktype(st[r1 -- sk, val][r -- j '], ty, st[r1 -- sk, val])) ↔ okarray(r, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ 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 3:
⊦ oktype(val0, ty, st[r1 -- sk, val]) ↔ oktype(val0, ty, st)
Proof step 4:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 19:
⊦ r = r1, r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ is_arraytype(st[r -- _type] .type) ∧ st[r -- _type] .type .type ≤ ty ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → okval(st[r -- j '], ty)) ↔ okarray(r, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_arrayref (r, i, st[r0 -- sk, val0]) ↔ is_arrayref(r, i, st))], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ r ≠ r0 → ( r -- sk ∈ st[r0 -- sk0, val] ↔ r -- sk ∈ st)], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]