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Proof step 22 from proof okarray-putba (previous step)

st[r0 -- _length] = intval(i), r0 -- _length ∈ st, 0 ≤ i, r0 ∈ st ⊦ r0 = jvmref, r = r0, r0 -- _type ∈ st ∧ is_typevalue(st[r0 -- _type]) ∧ is_arraytype(st[r0 -- _type] .type) ∧ st[r0 -- _type] .type .type ≤ ty ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r0 -- j ' ∈ st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty)) ↔ okreftype(refval(r0), mkarraytype(ty), st) ∧ (∀ j. 0 ≤ j ∧ j < i → r0 -- j ' ∈ st) ∧ (∀ j. 0 ≤ j ∧ j < i → okval(st[r0 -- j '], ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ 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 21:
st[r0 -- _length] = intval(i), r0 -- _length ∈ st, 0 ≤ i, r0 ∈ st, r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), is_arraytype(st[r0 -- _type] .type), st[r0 -- _type] .type .type ≤ ty, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r0 -- j ' ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r = r0, okreftype(refval(r0), mkarraytype(ty), st) ∧ (0 ≤ j ∧ j < i → r0 -- j ' ∈ st) ∧ (0 ≤ j0 ∧ j0 < i → okval(st[r0 -- j0 '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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))])]]