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Proof step 18 from proof contains-objectarray (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ contains(str, mkarraytype(ty), ty0) ↔ ty0 ≤ ty ∧ type∃(str, ty) ∧ type∃(str, ty0) ∨ contains(str, ty, ty0)
Proof step 17:
ty2 .jtelemtype = mkclasstype(`java.lang.Object' .class), type∃(str, ty0), is_classtype(ty0) ∨ is_arraytype(ty0), ∀ ty0, str, ty. i→n(ty .jtdims) < i→n(mkarraytype(ty2) .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)) ⊦ ty0 ≤ mkarraytype(ty2) ∧ type∃(str, mkarraytype(ty2)) ∧ type∃(str, ty0) ∨ contains(str, mkarraytype(ty2), ty0), contains(str, mkclasstype(`java.lang.Object' .class), ty0)

Rule argument

[crewrite-arg: contains-array-elemtype-08 , F , [ty0, ty, str] → [ty0, mkarraytype(ty2), str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty0, mkarraytype(ty2), str)]]