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Proof step 36 from proof validref-subspec-samesubclasses (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ has_classtype(st[r -- _type] .type) ∧ r ≠ jvmref → (junkref(str, r, st) ↔ junkref(str0, r, st))
Proof step 35:
¬ (¬ has_classtype(st[r -- _type] .type) ∧ r ≠ jvmref), st[r -- _type] = typeval(mkarraytype(ty0)), r -- _type ∈ st, junkref(str, r, st), same-subclasses(`java.lang.Object' .class, str, str0), r ∈ st, ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, junkref(str0, r, st), same-subclasses(ty0 .jtelemtype .class, str, str0) ∧ (contains(str0, mkclasstype(ty0 .jtelemtype .class), mkclasstype(class)) → same-subclasses(class, str, str0))

Rule argument

[speclemmaarg: , ¬ has_classtype(st[r -- _type] .type) ∧ r ≠ jvmref → (junkref(str, r, st) ↔ junkref(str0, r, st)) ,[str0, st, r, str] → [str0, st, r, str0] ,F ,junkrefs , ,junkref-not-hasclasstype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ has_classtype (st[r -- _type] .type) ∧ r ≠ jvmref ∧ ¬ junkref(str, r, st) → ¬ junkref(str0, r, st)])], [EXTRATERMS : (str0, st, r, str0)]]