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Proof step 8 from proof okarray-put-okval-01 (previous step)

st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(j), 0 ≤ j, r -- _length ∈ st, ty0 ≤ ty, r -- _type ∈ st, okval(val0, ty), is_arrayref(r, j, st), r ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st[r -- i ', val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 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)

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st[r -- i ', val0], mkarraytype(ty), refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ r -- _type ∈ st[r0 -- i ', val0] ↔ r -- _type ∈ st], [CSIMPSEQ : ⊦ (st[r -- i ', val][r0 -- _type]) = st[r0 -- _type]], [CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0])], [EXTRATERMS : (st[r -- i ', val0], mkarraytype(ty), refval(r))]]