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Proof step 173 from proof contains-subspec-better (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 172:
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 '), mkfs(class, ty2, fieldvar) ' ∈ instfields(class0), ty3 ≤ ty2, class+∃(str0, class0), is_classtype(ty), class0 ≤ ty .class, type∃(str, ty), same-subclasses(ty .class, str, str0), ∀ 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) ⊦ ty ∈ tys1, dups(tys1), ty3 ∈ tys1, interface∃(str0, class0), contains(str, ty, ty0), type∃(str, ty3), contains(str0, ty, ty3 .jtelemtype), ∃ 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ is_classtype(ty) → ty .jtelemtype = ty], [CSIMPSEQ : ⊦ is_classtype(ty) → is_reftype(ty)], [CSIMPSEQ : ⊦ mkclasstype(class) ≤ ty ↔ is_classtype(ty) ∧ class ≤ ty .class], [CSIMPSEQ : ⊦ ¬ interface∃(str, class) → ( tdname+∃(str, class) ↔ class+∃(str, class))], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)])]]