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Proof step 46 from proof compat-addobj (previous step)

st[_mode] = throw(r0, ty), st[r0 -- _type] = typeval(ty0), r0 ∈ st, asgcomp(str, refval(r0), ty, st), is_reftype(ty0), r0 -- _type ∈ st, okval(refval(r0), ty), ty ≤ mkclasstype(`java.lang.Throwable' .class), is_predefined_class(class), newref(r, st), _mode ∈ st, compatstatic(str, st), compatrefs(str, st), is_classtype(ty0) → class+∃(str, ty0 .class), has_classtype(ty0) → tdname+∃(str, ty0 .jtelemtype .class), has_classtype(ty) → tdname+∃(str, ty .jtelemtype .class) ⊦ r = jvmref, r0 = jvmref, compat(str, refval(r0), ty, st[r -- _type, typeval(mkclasstype(class))]) ∧ (has_classtype(ty) → class∃(str, ty .jtelemtype .class) ∨ interface∃(str, ty .jtelemtype .class) ∨ is_predefined_class(ty .jtelemtype .class))

User applied rule case distinction

And obtained the following new goals

Proof step 45:
st[_mode] = throw(r0, ty), st[r0 -- _type] = typeval(ty0), r0 ∈ st, asgcomp(str, refval(r0), ty, st), is_reftype(ty0), r0 -- _type ∈ st, okval(refval(r0), ty), ty ≤ mkclasstype(`java.lang.Throwable' .class), is_predefined_class(class), newref(r, st), _mode ∈ st, compatstatic(str, st), compatrefs(str, st), is_classtype(ty0) → class+∃(str, ty0 .class), has_classtype(ty0) → tdname+∃(str, ty0 .jtelemtype .class), has_classtype(ty) → tdname+∃(str, ty .jtelemtype .class) ⊦ compat(str, refval(r0), ty, st[r -- _type, typeval(mkclasstype(class))]), r = jvmref, r0 = jvmref

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)])]]