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Proof step 58 from proof validref-subspec-samesubclasses (previous step)

st[r -- _type] = typeval(ty), tdname+∃(str0, class), same-subclasses-contains(class, str, str0), junkref(str, r, st), r -- _type ∈ st, ty ≤ mkclasstype(class), r ∈ st ⊦ r = jvmref, is_arraytype(ty), junkref(str0, r, st), same-subclasses-contains(ty .class, str, str0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ class ≠ `java.lang.Object' .class → (ty ≤ mkclasstype(class) ↔ is_classtype(ty) ∧ ty .class ≤ class)
Proof step 52:
¬ class ≠ `java.lang.Object' .class, st[r -- _type] = typeval(ty), tdname+∃(str0, class), same-subclasses-contains(class, str, str0), junkref(str, r, st), r -- _type ∈ st, ty ≤ mkclasstype(class), r ∈ st ⊦ r = jvmref, is_arraytype(ty), junkref(str0, r, st), same-subclasses-contains(ty .class, str, str0)
Proof step 57:
class ≠ `java.lang.Object' .class, st[r -- _type] = typeval(ty), tdname+∃(str0, class), same-subclasses-contains(class, str, str0), junkref(str, r, st), r -- _type ∈ st, is_classtype(ty) ∧ ty .class ≤ class, r ∈ st ⊦ r = jvmref, is_arraytype(ty), junkref(str0, r, st), same-subclasses-contains(ty .class, str, str0)

Rule argument

[speclemmaarg: , class ≠ `java.lang.Object' .class → (ty ≤ mkclasstype(class) ↔ is_classtype(ty) ∧ ty .class ≤ class) ,[class, ty] → [class, ty] ,F ,typefuns , ,subclass-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (class, ty)]]