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Proof step 72 from proof same-subclasses-forward (previous step)

same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty3), is_reftype(ty), type∃(str0, ty), type∃(str0, ty1), type∃(str0, ty3), ty1 ≤ ty, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ class0. contains(str0, mkclasstype(ty .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ contains(str0, ty, ty3), same-subclasses(ty3 .jtelemtype .class, str, str0) ∧ (contains(str0, ty3 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

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 71:
same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty3), is_reftype(ty), type∃(str0, ty), type∃(str0, ty1), type∃(str0, ty3), ty1 ≤ ty, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ class0. contains(str0, mkclasstype(ty .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ type∃(str0, ty) ∧ is_reftype(ty) ∧ ( (∃ ty1. ty1 ≤ ty ∧ type∃(str0, ty1) ∧ type∃(str0, ty3) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty3 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty3 ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ ty ∧ 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, ty3))), same-subclasses(ty3 .jtelemtype .class, str, str0) ∧ (contains(str0, ty3 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

Rule argument

[crewrite-arg: contains-type-rec, F, [ty0, ty, str] → [ty3, ty, str0]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty3, ty, str0)]]