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Proof step 9 from proof compatval-addclass (previous step)

fis .keys = statfields(class), okfieldinits(class, fis), okval(refval(r), ty), r ≠ jvmref → r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ is_reftype(st[r -- _type] .type) ∧ (has_classtype(st[r -- _type] .type) → tdname+∃(str, st[r -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[r -- _type] .type) → class+∃(str, st[r -- _type] .type .class)) ∧ asgcomp(str, refval(r), ty, st) ⊦ (ty = void_type ∨ is_reftype(ty)) ∧ ( r ≠ jvmref → r -- _type ∈ addclass(class, fis, st) ∧ is_typevalue(st[r -- _type]) ∧ is_reftype(st[r -- _type] .type) ∧ ( has_classtype(st[r -- _type] .type) → class∃(str, st[r -- _type] .type .jtelemtype .class) ∨ interface∃(str, st[r -- _type] .type .jtelemtype .class) ∨ is_predefined_class(st[r -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[r -- _type] .type) → class+∃(str, st[r -- _type] .type .class)) ∧ is_subtype(str, st[r -- _type] .type, ty))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
st[r -- _type] = typeval(ty0) ∧ is_typevalue(st[r -- _type]), fis .keys = statfields(class), okfieldinits(class, fis), okval(refval(r), ty), r ≠ jvmref → r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ is_reftype(ty0) ∧ (has_classtype(ty0) → tdname+∃(str, ty0 .jtelemtype .class)) ∧ (is_classtype(ty0) → class+∃(str, ty0 .class)) ∧ asgcomp(str, refval(r), ty, st) ⊦ (ty = void_type ∨ is_reftype(ty)) ∧ ( r ≠ jvmref → r -- _type ∈ addclass(class, fis, st) ∧ is_typevalue(st[r -- _type]) ∧ is_reftype(ty0) ∧ ( has_classtype(ty0) → class∃(str, ty0 .jtelemtype .class) ∨ interface∃(str, ty0 .jtelemtype .class) ∨ is_predefined_class(ty0 .jtelemtype .class)) ∧ (is_classtype(ty0) → class+∃(str, ty0 .class)) ∧ is_subtype(str, ty0, ty))

Rule argument

[speclemmaarg: ,is_typevalue(val) → (ty = val .type ↔ val = typeval(ty)) ,[val, ty] → [st[r -- _type], ty0] ,T ,javavalue , ,elim-10 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ okval(refval(r), ty) ↔ ty = void_type ∨ is_reftype(ty)], [CSIMPELIM : ⊦ is_typevalue(val) → ( ty = val .type ↔ val = typeval(ty))])], [EXTRATERMS : (st[r -- _type], ty0)]]