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Proof step 12 from proof okarray-put-samefield-01 (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty1)), is_arrayref(r, i, st), r -- _length ∈ st, ty1 ≤ ty, r -- _type ∈ st, r ∈ st, okval(val, ty0), okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, 0 ≤ i, ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ okreftype(refval(r), mkarraytype(ty), st), r = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 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, mkarraytype(ty), refval(r)] ]

Additional information

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