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Proof step 16 from proof okarray-putba (previous step)

st[r0 -- _length] = intval(i), st[r0 -- _type] = typeval(mkarraytype(ty0)), r0 -- _length ∈ st, 0 ≤ i, r0 ∈ st, r0 -- _type ∈ st, ty0 ≤ ty, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r0 -- j ' ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r = r0, is_referencevalue(refval(r0)) ∧ ( refval(r0) .refval ≠ jvmref → refval(r0) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r0) .refval -- _type]) ∧ st[refval(r0) .refval -- _type] .type ≤ mkarraytype(ty)) ∧ (0 ≤ j ∧ j < i → r0 -- j ' ∈ st) ∧ (0 ≤ j0 ∧ j0 < i → okval(st[r0 -- j0 '], ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(i), ty0 ≤ ty, r0 -- _type ∈ st, r0 ∈ st, 0 ≤ i, r0 -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r0 -- j ' ∈ st ⊦ r = r0, r0 = jvmref, (0 ≤ j ∧ j < i → r0 -- j ' ∈ st) ∧ (0 ≤ j0 ∧ j0 < i → okval(st[r0 -- j0 '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]