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Proof step 34 from proof contains-objectarray (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 12:
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)
Proof step 33:
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

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]