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Proof step 12 from proof same-subclasses-forward (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ contains(str, ty, ty1) ∧ ty ≤ ty0 ∧ type∃(str, ty0) → contains(str, ty0, ty1)

Rule argument

[crewrite-arg: contains-supertype-04 , F , [str, ty, ty1, ty0] → [str0, ty3 .jtelemtype, mkclasstype(class0), ty .jtelemtype] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ type∃(str, ty .jtelemtype) → ¬ type∃(str, ty)])], [EXTRATERMS : (str0, ty3 .jtelemtype, mkclasstype(class0), ty .jtelemtype)]]