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Proof step 192 from proof contains-subspec-better (previous step)

type∃(str0, ty3), tys + ty0 ' = ty3 ' + tys1, contains(str0, ty, ty0), type∃(str0, ty0), has_classtype(ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), contains(str0, ty3 ' + tys1), type∃(str0, ty), type∃(str, ty0), type∃(str0, ty3), ty3 ∈ tys, ty0 ∈ tys1, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ type∃(str, ty3), contains(str, ty, ty0), dups(tys), ty ∈ tys

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 130:
⊦ same-subclasses-contains(class, str, str0) ↔ same-subclasses(class, str, str0) ∧ (∀ class0. contains(str0, mkclasstype(class), mkclasstype(class0)) → same-subclasses(class0, str, str0))
Proof step 191:
type∃(str0, ty3), tys + ty0 ' = ty3 ' + tys1, contains(str0, ty, ty0), type∃(str0, ty0), has_classtype(ty), same-subclasses(ty .jtelemtype .class, str, str0) ∧ (∀ class0. contains(str0, mkclasstype(ty .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0)), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), contains(str0, ty3 ' + tys1), type∃(str0, ty), type∃(str, ty0), type∃(str0, ty3), ty3 ∈ tys, ty0 ∈ tys1, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ type∃(str, ty3), contains(str, ty, ty0), dups(tys), ty ∈ tys

Rule argument

[crewrite-arg: same-subclasses-all-def , F , [str0, str, class] → [str0, str, ty .jtelemtype .class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str0, str, ty .jtelemtype .class)]]