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Proof step 37 from proof compat-addobj (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 36:
st[r0 -- _type] = typeval(ty0), 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), okval(refval(r0), ty), r0 -- _type ∈ st, is_reftype(ty0), r0 ∈ st, ty0 ≤ ty, ty0 ≤ mkclasstype(`java.lang.Throwable' .class), is_classtype(ty0) → class+∃(str, ty0 .class), has_classtype(ty0) → tdname+∃(str, ty0 .jtelemtype .class), has_classtype(ty) → tdname+∃(str, ty .jtelemtype .class) ⊦ r0 -- _type = r -- _type, r0 = jvmref, r = jvmref, (ty = void_type ∨ is_reftype(ty)) ∧ is_typevalue(st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) ∧ is_reftype((st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) .type) ∧ ( is_classtype((st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) .type) → class+∃(str, (st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) .type .class)) ∧ (st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) .type ≤ ty ∧ ( has_classtype((st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) .type) → class∃(str, (st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) .type .jtelemtype .class) ∨ interface∃(str, (st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) .type .jtelemtype .class) ∨ is_predefined_class((st[r -- _type, typeval(mkclasstype(class))][r0 -- _type]) .type .jtelemtype .class)) ∧ (has_classtype(ty) → class∃(str, ty .jtelemtype .class) ∨ interface∃(str, ty .jtelemtype .class) ∨ is_predefined_class(ty .jtelemtype .class))

Rule argument

[fma-arg: r0 -- _type = r -- _type]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ newref(r, st) ∧ r0 ∈ st → r ≠ r0])], [EXTRAFMAS : (r0 -- _type = r -- _type)]]