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Proof step 33 from proof compat-addobj (previous step)

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

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_reftype(ty) → ¬ has_classtype(ty)], [CSIMPSEQ : ⊦ okval(refval(r), ty) ↔ ty = void_type ∨ is_reftype(ty)], [CSIMPSEQ : ⊦ ¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0)], [CSIMPSEQ : ⊦ ¬ is_reftype(ty) → (ty ≤ ty0 ↔ ty = ty0)], [CSIMPSEQ : ⊦ ¬ has_classtype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)])]]