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Proof step 16 from proof validref-subspec-samesubclasses (previous step)

st[r -- _type] = typeval(mkarraytype(ty0)), has_classtype(ty0), r -- _type ∈ st, junkref(str, r, st), same-subclasses(`java.lang.Object' .class, str, str0), r ∈ st, is_valid_ref(str0, r, st), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, tdname+∃(str0, ty0 .jtelemtype .class), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, junkref(str0, r, st), same-subclasses(ty0 .jtelemtype .class, str, str0) ∧ (contains(str0, ty0 .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ¬ type∃(str, st[r -- _type] .type) ∧ r ≠ jvmref → ¬ is_valid_ref(str, r, st)
Proof step 15:
¬ (¬ type∃(str0, st[r -- _type] .type) ∧ r ≠ jvmref), st[r -- _type] = typeval(mkarraytype(ty0)), has_classtype(ty0), r -- _type ∈ st, junkref(str, r, st), same-subclasses(`java.lang.Object' .class, str, str0), r ∈ st, is_valid_ref(str0, r, st), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, tdname+∃(str0, ty0 .jtelemtype .class), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, junkref(str0, r, st), same-subclasses(ty0 .jtelemtype .class, str, str0) ∧ (contains(str0, ty0 .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0))

Rule argument

[speclemmaarg: , ¬ type∃(str, st[r -- _type] .type) ∧ r ≠ jvmref → ¬ is_valid_ref(str, r, st) ,[st, r, str] → [st, r, str0] ,F ,addfuns , ,is_valid_ref-typeex ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str0)]]