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Proof step 85 from proof same-subclasses-array-forward (previous step)

st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), st[r0 -- _type] .type = mkarraytype(ty0), i < st[r -- _length] .intval, same-subclasses(`java.lang.Object' .class, str, str0), is_array(str, r, st), has_classtype(ty), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, contains(str0, mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype), junkref(str0, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 61:
⊦ contains(str, ty, ty0) ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ ( (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ type∃(str, ty0) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str, ty2, ty0)))
Proof step 84:
st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), st[r0 -- _type] .type = mkarraytype(ty0), i < st[r -- _length] .intval, same-subclasses(`java.lang.Object' .class, str, str0), is_array(str, r, st), has_classtype(ty), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, type∃(str0, mkclasstype(`java.lang.Object' .class)) ∧ is_reftype(mkclasstype(`java.lang.Object' .class)) ∧ ( (∃ ty1. ty1 ≤ mkclasstype(`java.lang.Object' .class) ∧ type∃(str0, ty1) ∧ type∃(str0, ty0 .jtelemtype) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 .jtelemtype ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 .jtelemtype ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ mkclasstype(`java.lang.Object' .class) ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, ty0 .jtelemtype))), junkref(str0, r, st)

Rule argument

[crewrite-arg: contains-type-rec , F , [ty0, ty, str] → [ty0 .jtelemtype, mkclasstype(`java.lang.Object' .class), str0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty0 .jtelemtype, mkclasstype(`java.lang.Object' .class), str0)]]