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Proof step 45 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) ⊦ compat(str, refval(r0), ty, st[r -- _type, typeval(mkclasstype(class))]), r = jvmref, r0 = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ compat(str, val, ty, st) ↔ okval(val, ty) ∧ ( is_referencevalue(val) ∧ val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ is_reftype(st[val .refval -- _type] .type) ∧ (has_classtype(st[val .refval -- _type] .type) → tdname+∃(str, st[val .refval -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[val .refval -- _type] .type) → class+∃(str, st[val .refval -- _type] .type .class)) ∧ asgcomp(str, val, ty, st))
Proof step 44:
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) ⊦ okval(refval(r0), ty) ∧ ( is_referencevalue(refval(r0)) ∧ refval(r0) .refval ≠ jvmref → refval(r0) .refval -- _type ∈ st[r -- _type, typeval(mkclasstype(class))] ∧ is_typevalue(st[r -- _type, typeval(mkclasstype(class))][refval(r0) .refval -- _type]) ∧ is_reftype((st[r -- _type, typeval(mkclasstype(class))][refval(r0) .refval -- _type]) .type) ∧ ( has_classtype((st[r -- _type, typeval(mkclasstype(class))][refval(r0) .refval -- _type]) .type) → tdname+∃(str, (st[r -- _type, typeval(mkclasstype(class))][refval(r0) .refval -- _type]) .type .jtelemtype .class)) ∧ ( is_classtype((st[r -- _type, typeval(mkclasstype(class))][refval(r0) .refval -- _type]) .type) → class+∃(str, (st[r -- _type, typeval(mkclasstype(class))][refval(r0) .refval -- _type]) .type .class)) ∧ asgcomp(str, refval(r0), ty, st[r -- _type, typeval(mkclasstype(class))])), r = jvmref, r0 = jvmref

Rule argument

[crewrite-arg: value-compat , F , [st, ty, val, str] → [st[r -- _type, typeval(mkclasstype(class))], ty, refval(r0), str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- _type, typeval(mkclasstype(class))], ty, refval(r0), str)]]