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Proof step 48 from proof cyclic-addrefarray (previous step)

cyclic(str, r, addarray(r, ty, vals, st)), newref(r, st), type∃(str, ty), is_reftype(ty), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ ¬ cyclic(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 47:
∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, (addarray(r, ty, vals, st)[r -- _type]) .type, addarray(r, ty, vals, st)), newref(r, st), type∃(str, ty), is_reftype(ty), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ ¬ cyclic(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, r = jvmref

Rule argument

[crewrite-arg: cyclic-def-simple , F , [st, r, str] → [addarray(r, ty, vals, st), r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, ty, vals, st), r, str)]]