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Proof step 117 from proof same-subclasses-01 (previous step)

ty0 .jtelemtype = mkclasstype(class3), same-subclasses(class3, str, str0), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), # tys ≤ # tys1, contains(str0, mkclasstype(class3) ' + tys + mkclasstype(class0) '), contains(str0, mkclasstype(class3), mkclasstype(class4)), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2), same-subclasses(class4, str, str0), contains(str0, mkclasstype(class), mkclasstype(class4)), ∃ 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), (∃ fs. fs ' ∈ instfields(class2) ∧ ty0 ≤ fs .type) ∧ contains(str0, ty0, mkclasstype(class3))

User applied rule case distinction

And obtained the following new goals

Proof step 113:
ty0 .jtelemtype = mkclasstype(class3), same-subclasses(class3, str, str0), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), # tys ≤ # tys1, contains(str0, mkclasstype(class3) ' + tys + mkclasstype(class0) '), contains(str0, mkclasstype(class3), mkclasstype(class4)), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ ∃ fs. fs ' ∈ instfields(class2) ∧ ty0 ≤ fs .type, class = `java.lang.Object' .class, is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2), same-subclasses(class4, str, str0), contains(str0, mkclasstype(class), mkclasstype(class4)), ∃ 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)
Proof step 116:
ty0 .jtelemtype = mkclasstype(class3), same-subclasses(class3, str, str0), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), # tys ≤ # tys1, contains(str0, mkclasstype(class3) ' + tys + mkclasstype(class0) '), contains(str0, mkclasstype(class3), mkclasstype(class4)), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ contains(str0, ty0, mkclasstype(class3)), class = `java.lang.Object' .class, is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2), same-subclasses(class4, str, str0), contains(str0, mkclasstype(class), mkclasstype(class4)), ∃ 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)

Rule argument

[CASEDARG : pos: right 8, ()]

Additional information

[[CONCRETESIMPRULES : ()]]