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Proof step 9 from proof okarray-put-07 (previous step)

st[r0 -- _length] = intval(i), st[r0 -- _type] = typeval(mkarraytype(ty0)), 0 ≤ i, r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, is_arrayref(r0, i, st), r0 ∈ 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 → okval(st[r0 -- j '], ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(i), r0 ∈ st, is_arrayref(r0, i, st), r0 -- _length ∈ st, ty0 ≤ ty, r0 -- _type ∈ st, 0 ≤ i, j < i, 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty) ⊦ r = r0, r0 = jvmref, okval(st[r0 -- j '], ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [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))])]]