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Proof step 41 from proof cyclic-addrefarray (previous step)

newref(r, st), type∃(str, ty), is_reftype(ty), validrefs(str, r ' + refs0, mkarraytype(ty), addarray(r, ty, vals, st)), is_obj(str, r, addarray(r, ty, vals, st)) ∨ is_array(str, r, addarray(r, ty, vals, st)), ∀ 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, ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_arraytype(st[r -- _type] .type) → ¬ is_obj(str, r, st)
Proof step 40:
is_arraytype((addarray(r, ty, vals, st)[r -- _type]) .type), newref(r, st), type∃(str, ty), is_reftype(ty), validrefs(str, r ' + refs0, mkarraytype(ty), addarray(r, ty, vals, st)), false ∨ is_array(str, r, addarray(r, ty, vals, st)), ∀ 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, ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[speclemmaarg: ,is_arraytype(st[r -- _type] .type) → ¬ is_obj(str, r, st) ,[st, r, str] → [addarray(r, ty, vals, st), r, str] ,F ,addfuns , ,is_obj-arraytype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _type ] ) = typeval(mkarraytype(ty))], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))])], [EXTRATERMS : (addarray(r, ty, vals, st), r, str)]]