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Proof step 15 from proof validref-subspec-samesubclasses (previous step)

¬ (¬ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
st[r -- _type] = typeval(mkarraytype(ty0)), is_valid_ref(str0, r, st), r ∈ st, same-subclasses(`java.lang.Object' .class, str, str0), junkref(str, r, st), r -- _type ∈ st, has_classtype(ty0), type∃(str0, ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, junkref(str0, r, st), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, tdname+∃(str0, ty0 .jtelemtype .class), same-subclasses(ty0 .jtelemtype .class, str, str0) ∧ (contains(str0, ty0 .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ type∃(str, mkarraytype(ty)) ↔ type∃(str, ty)], [CSIMPSEQ : ⊦ typeval(ty) .type = ty])]]