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Proof step 20 from proof okarray-del (previous step)

⊦ r = r0, okreftype(refval(r0), mkarraytype(ty), st -- r) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st -- r ∧ is_integervalue((st -- r)[r0 -- _length]) ∧ 0 ≤ (st -- r)[r0 -- _length] .intval ∧ is_arrayref(r0, (st -- r)[r0 -- _length] .intval, st -- r) ∧ (∀ j. 0 ≤ j ∧ j < (st -- r)[r0 -- _length] .intval → oktype((st -- r)[r0 -- j '], ty, st -- r)) ↔ okarray(r0, 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(val, ty, st -- r) ↔ oktype(val, ty, st)
Proof step 4:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 19:
⊦ r = r0, r0 -- _type ∈ st ∧ is_typevalue(st[r0 -- _type]) ∧ is_arraytype(st[r0 -- _type] .type) ∧ st[r0 -- _type] .type .type ≤ ty ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r0 -- j '], ty)) ↔ okarray(r0, ty, st)

Rule argument

[emptyarg]

Additional information

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