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Proof step 22 from proof compat-throw-02 (previous step)

compatmode(str, st), compatstatic(str, st), compatrefs(str, st) ⊦ compat(str, refval(r), mkclasstype(class), st[_mode, throw(r, mkclasstype(class))]) ∧ is_subtype(str, mkclasstype(class), mkclasstype(`java.lang.Throwable' .class)) ↔ class ≤ `java.lang.Throwable' .class ∧ compat(str, refval(r), mkclasstype(class), st), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is_subtype(str, ty1, ty2) ↔ ty1 ≤ ty2 ∧ (has_classtype(ty1) → tdname+∃(str, ty1 .jtclass)) ∧ (has_classtype(ty2) → tdname+∃(str, ty2 .jtclass))
Proof step 21:
compatmode(str, st), compatstatic(str, st), compatrefs(str, st) ⊦ compat(str, refval(r), mkclasstype(class), st[_mode, throw(r, mkclasstype(class))]) ∧ mkclasstype(class) ≤ mkclasstype(`java.lang.Throwable' .class) ∧ (has_classtype(mkclasstype(class)) → tdname+∃(str, mkclasstype(class) .jtclass)) ∧ (has_classtype(mkclasstype(`java.lang.Throwable' .class)) → tdname+∃(str, mkclasstype(`java.lang.Throwable' .class) .jtclass)) ↔ class ≤ `java.lang.Throwable' .class ∧ compat(str, refval(r), mkclasstype(class), st), r = jvmref

Rule argument

[speclemmaarg: , is_subtype(str, ty1, ty2) ↔ ty1 ≤ ty2 ∧ (has_classtype(ty1) → tdname+∃(str, ty1 .jtclass)) ∧ (has_classtype(ty2) → tdname+∃(str, ty2 .jtclass)) ,[ty2, ty1, str] → [mkclasstype(`java.lang.Throwable' .class), mkclasstype(class), str] ,F ,typefuns , ,is_subtype-level ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (mkclasstype(`java.lang.Throwable' .class), mkclasstype(class), str)]]