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Proof step 105 from proof same-subclasses-array-forward (previous step)

st[r0 -- _type] .type = mkclasstype(class1), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), st[r -- i '] = refval(r0), st[r -- _type] .type = mkarraytype(ty), contains(str0, mkclasstype(class1), mkclasstype(class)), 0 ≤ i, 0 < st[r -- _length] .intval, has_classtype(ty), is_array(str, r, st), same-subclasses(`java.lang.Object' .class, str, str0), i < st[r -- _length] .intval, class1 ≤ `java.lang.Object' .class, ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, tdname+∃(str0, class), class ≤ `java.lang.Object' .class, same-subclasses(class, str, str0), junkref(str0, r, st), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 104:
⊦ ¬ type∃(str, ty0) → ¬ contains(str, ty, ty0)

Rule argument

[crewrite-arg: contains-typeex-03 , F , [ty0, ty, str] → [mkclasstype(class), mkclasstype(class1), str0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)], [CSIMPSEQ : ⊦ tdname+∃(str, class) → class ≤ `java.lang.Object' .class])], [EXTRATERMS : (mkclasstype(class), mkclasstype(class1), str0)]]