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Proof step 41 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, (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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ asgcomp(str, val, ty, st) ↔ ¬ is_referencevalue(val) ∨ val .refval = jvmref ∨ is_subtype(str, st[val .refval -- _type] .type, ty)
Proof step 40:
st[_mode] = throw(r0, ty), st[r0 -- _type] = typeval(ty0), r0 ∈ st, ¬ is_referencevalue(refval(r0)) ∨ refval(r0) .refval = jvmref ∨ is_subtype(str, st[refval(r0) .refval -- _type] .type, ty), 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, (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

[speclemmaarg: , asgcomp(str, val, ty, st) ↔ ¬ is_referencevalue(val) ∨ val .refval = jvmref ∨ is_subtype(str, st[val .refval -- _type] .type, ty) ,[st, ty, val, str] → [st, ty, refval(r0), str] ,F ,okfuns , ,asgcomp ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, refval(r0), str)]]