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Proof step 52 from proof compat-addobj (previous step)

st[_mode] = throw(r0, ty), compatrefs(str, st), compatstatic(str, st), _mode ∈ st, newref(r, st), is_predefined_class(class), is_subtype(str, ty, mkclasstype(`java.lang.Throwable' .class)), compat(str, refval(r0), ty, st) ⊦ r0 = jvmref, r = jvmref, compat(str, refval(r0), ty, st[r -- _type, typeval(mkclasstype(class))]) ∧ ty ≤ mkclasstype(`java.lang.Throwable' .class) ∧ (has_classtype(ty) → class∃(str, ty .jtelemtype .class) ∨ interface∃(str, ty .jtelemtype .class) ∨ is_predefined_class(ty .jtelemtype .class))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ is_subtype(str, ty1, ty2) ↔ ty1 ≤ ty2 ∧ (has_classtype(ty1) → tdname+∃(str, ty1 .jtclass)) ∧ (has_classtype(ty2) → tdname+∃(str, ty2 .jtclass))
Proof step 51:
st[_mode] = throw(r0, ty), compatrefs(str, st), compatstatic(str, st), _mode ∈ st, newref(r, st), is_predefined_class(class), ty ≤ mkclasstype(`java.lang.Throwable' .class) ∧ (has_classtype(ty) → tdname+∃(str, ty .jtclass)) ∧ (has_classtype(mkclasstype(`java.lang.Throwable' .class)) → tdname+∃(str, mkclasstype(`java.lang.Throwable' .class) .jtclass)), compat(str, refval(r0), ty, st) ⊦ r0 = jvmref, r = jvmref, compat(str, refval(r0), ty, st[r -- _type, typeval(mkclasstype(class))]) ∧ ty ≤ mkclasstype(`java.lang.Throwable' .class) ∧ (has_classtype(ty) → class∃(str, ty .jtelemtype .class) ∨ interface∃(str, ty .jtelemtype .class) ∨ is_predefined_class(ty .jtelemtype .class))

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), ty, str] ,F ,typefuns , ,is_subtype-level ]

Additional information

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