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Proof step 69 from proof same-subclasses-01 (previous step)

class3 ≤ class4, mkfs(class1, mkclasstype(class4), fieldvar) ' ∈ instfields(class2), contains(str0, (mkclasstype(class3) ' + tys1) + mkclasstype(class0) '), tdname+∃(str0, class2), class2 ≤ class, tdname+∃(str0, class), same-subclasses(class, str, str0), ∀ class0. contains(str0, mkclasstype(class), mkclasstype(class0)) → same-subclasses(class0, str, str0), ∀ class0, str0, str, class, tys0. # tys0 < # (mkclasstype(class3) + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, type∃(str0, mkclasstype(class)) ∧ is_reftype(mkclasstype(class)) ∧ ( (∃ ty1. ty1 ≤ mkclasstype(class) ∧ type∃(str0, ty1) ∧ type∃(str0, mkclasstype(class3)) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ mkclasstype(class3) ≤ fs .type)) ∧ (is_arraytype(ty1) → mkclasstype(class3) ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ mkclasstype(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, mkclasstype(class3)))), interface∃(str0, class2), tdname+∃(str, class0), same-subclasses(class3, str, str0) ∧ (contains(str0, mkclasstype(class3), mkclasstype(class5)) → same-subclasses(class5, str, str0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
class3 ≤ class4, mkfs(class1, mkclasstype(class4), fieldvar) ' ∈ instfields(class2), contains(str0, (mkclasstype(class3) ' + tys1) + mkclasstype(class0) '), tdname+∃(str0, class2), class2 ≤ class, tdname+∃(str0, class), same-subclasses(class, str, str0), ∀ class0. contains(str0, mkclasstype(class), mkclasstype(class0)) → same-subclasses(class0, str, str0), ∀ class0, str0, str, class, tys0. # tys0 < # (mkclasstype(class3) + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, interface∃(str0, class2), tdname+∃(str, class0), same-subclasses(class3, str, str0) ∧ (contains(str0, mkclasstype(class3), mkclasstype(class5)) → same-subclasses(class5, str, str0)), ∃ ty. ty ≤ mkclasstype(class) ∧ type∃(str0, ty) ∧ tdname+∃(str0, class3) ∧ (is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ (∃ fs. fs ' ∈ instfields(ty .class) ∧ mkclasstype(class3) ≤ fs .type)) ∧ (is_arraytype(ty) → mkclasstype(class3) ≤ ty .type), ∃ ty1, ty2. ty1 ≤ mkclasstype(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, mkclasstype(class3))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_reftype(mkclasstype(class))], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)])]]