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Proof step 174 from proof contains-subspec-better (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 173:
ty1 = mkclasstype(class0), type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty), type∃(str0, ty0), contains(str0, ty, ty0), has_classtype(ty3), type∃(str0, ty3), type∃(str, ty0), type∃(str0, ty), contains(str0, (ty3 ' + tys1) + ty0 '), is_classtype(ty1), mkfs(class, ty2, fieldvar) ' ∈ instfields(class0), ty3 ≤ ty2, ∀ ty0, str0, str, ty, tys0. # tys0 < # (ty3 + tys1) → ( 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) ⊦ contains(str, ty, ty0), type∃(str, ty3), contains(str0, ty .jtelemtype, ty3 .jtelemtype), ty ∈ tys1, dups(tys1), ty3 ∈ tys1, interface∃(str0, class0), ∃ 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), ∃ fs. fs ' ∈ instfields(class0) ∧ ty3 ≤ fs .type

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [ty1, class0] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (ty1, class0)]]