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Proof step 28 from proof validref-subspec-samesubclasses (previous step)

st[r -- _type] = typeval(mkarraytype(ty0)), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, r ∈ st, same-subclasses(`java.lang.Object' .class, str, str0), junkref(str, r, st), r -- _type ∈ st, has_classtype(ty0), contains(str0, ty0 .jtelemtype, mkclasstype(class)) ⊦ r = jvmref, junkref(str0, r, st), same-subclasses(class, str, str0), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class)), ty0 .jtelemtype ≤ mkclasstype(`java.lang.Object' .class)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ type∃(str, ty) → (ty ≤ mkclasstype(`java.lang.Object' .class) ↔ is_classtype(ty) ∨ is_arraytype(ty))
Proof step 24:
⊦ ¬ type∃(str, ty) → ¬ contains(str, ty, ty0)
Proof step 27:
type∃(str0, ty0 .jtelemtype), st[r -- _type] = typeval(mkarraytype(ty0)), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, r ∈ st, same-subclasses(`java.lang.Object' .class, str, str0), junkref(str, r, st), r -- _type ∈ st, has_classtype(ty0), contains(str0, ty0 .jtelemtype, mkclasstype(class)) ⊦ r = jvmref, junkref(str0, r, st), same-subclasses(class, str, str0), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class)), is_classtype(ty0 .jtelemtype) ∨ is_arraytype(ty0 .jtelemtype)

Rule argument

[speclemmaarg: , type∃(str, ty) → ( ty ≤ mkclasstype(`java.lang.Object' .class) ↔ is_classtype(ty) ∨ is_arraytype(ty)) ,[str, ty] → [str0, ty0 .jtelemtype] ,F ,typefuns , ,subtype-object ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str0, ty0 .jtelemtype)]]