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Proof step 12 from proof contains-objectarray (previous step)

contains(str, ty, ty0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class) ⊦ type∃(str, ty0) ∧ (is_classtype(ty0) ∨ is_arraytype(ty0)) ∧ is_arraytype(ty) ∨ contains(str, mkclasstype(`java.lang.Object' .class), ty0)

User applied rule induction

And obtained the following new goals

Proof step 11:
contains(str, ty, ty0) ∧ ty .jtelemtype = mkclasstype(`java.lang.Object' .class), ∀ ty0, str, ty1. i→n(ty1 .jtdims) < i→n(ty .jtdims) → ( contains(str, ty1, ty0) ∧ ty1 .jtelemtype = mkclasstype(`java.lang.Object' .class) → type∃(str, ty0) ∧ (is_classtype(ty0) ∨ is_arraytype(ty0)) ∧ is_arraytype(ty1) ∨ contains(str, mkclasstype(`java.lang.Object' .class), ty0)) ⊦ type∃(str, ty0) ∧ (is_classtype(ty0) ∨ is_arraytype(ty0)) ∧ is_arraytype(ty) ∨ contains(str, mkclasstype(`java.lang.Object' .class), ty0)

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, i→n(ty .jtdims), [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (i→n(ty .jtdims))]]