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Proof step 18 from proof same-subclasses-forward (previous step)

is_classtype(ty .jtelemtype), contains(str0, ty, ty3), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty3), is_reftype(ty), type∃(str0, ty), type∃(str0, ty1), type∃(str0, ty3), ty1 ≤ ty, ty3 .jtelemtype ≤ ty .jtelemtype, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ ty .jtelemtype = mkclasstype(`java.lang.Object' .class), same-subclasses(ty3 .jtelemtype .class, str, str0), contains(str0, ty .jtelemtype, ty3 .jtelemtype), ty3 .jtelemtype .class ≤ ty .jtelemtype .class

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [ty .jtelemtype, class1] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class) = mkclasstype(class0) ↔ class = class0], [CSIMPSEQ : ⊦ class ≠ `java.lang.Object' .class → ( ty ≤ mkclasstype(class) ↔ is_classtype(ty) ∧ ty .class ≤ class)], [CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (ty .jtelemtype, class1)]]