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Proof step 33 from proof contains-objectarray (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 13:
⊦ contains(str, ty .jtelemtype, ty0) → contains(str, ty, ty0)
Proof step 32:
contains(str, ty .jtelemtype, ty0) → contains(str, ty, ty0), type∃(str, ty0) ∧ (is_classtype(ty0) ∨ is_arraytype(ty0)) ∧ is_arraytype(ty) ∨ contains(str, mkclasstype(`java.lang.Object' .class), ty0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class) ⊦ contains(str, ty, ty0)

Rule argument

[LEMMAARG : contains-array-elemtype-02, [str, ty, ty0] → [str, ty, ty0]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, ty, ty0)]]