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Proof step 20 from proof contains-objectarray (previous step)

ty1 .type .jtelemtype = mkclasstype(`java.lang.Object' .class), is_arraytype(ty1), type∃(str, ty0), is_classtype(ty0) ∨ is_arraytype(ty0), ∀ ty0, str, ty. i→n(ty .jtdims) < i→n(ty1 .jtdims) → ( ty .jtelemtype = mkclasstype(`java.lang.Object' .class) ∧ type∃(str, ty0) ∧ (is_classtype(ty0) ∨ is_arraytype(ty0)) → contains(str, mkclasstype(`java.lang.Object' .class), ty0) ∨ contains(str, mkarraytype(ty), ty0)) ⊦ contains(str, mkarraytype(ty1), ty0), contains(str, mkclasstype(`java.lang.Object' .class), ty0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
ty1 = mkarraytype(ty2), ty2 .jtelemtype = mkclasstype(`java.lang.Object' .class), is_arraytype(ty1), type∃(str, ty0), is_classtype(ty0) ∨ is_arraytype(ty0), ∀ ty0, str, ty. i→n(ty .jtdims) < i→n(ty1 .jtdims) → ( ty .jtelemtype = mkclasstype(`java.lang.Object' .class) ∧ type∃(str, ty0) ∧ (is_classtype(ty0) ∨ is_arraytype(ty0)) → contains(str, mkclasstype(`java.lang.Object' .class), ty0) ∨ contains(str, mkarraytype(ty), ty0)) ⊦ contains(str, mkarraytype(ty1), ty0), contains(str, mkclasstype(`java.lang.Object' .class), ty0)

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [ty1, ty2] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (ty1, ty2)]]