[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 159 from proof same-subclasses-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 147:
has_classtype(ty0), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses-contains(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), # tys ≤ # tys1, contains(str0, ty0 .jtelemtype ' + tys + mkclasstype(class0) '), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ same-subclasses-contains(ty0 .jtelemtype .class, str, str0) ∧ contains(str0, mkclasstype(ty0 .jtelemtype .class) ' + tys + mkclasstype(class0) '), class = `java.lang.Object' .class, is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2)
Proof step 158:
contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses-contains(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), # tys ≤ # tys1, contains(str0, ty0 .jtelemtype ' + tys + mkclasstype(class0) '), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ has_classtype(ty0), same-subclasses-contains(ty0 .jtelemtype .class, str, str0) ∧ contains(str0, mkclasstype(ty0 .jtelemtype .class) ' + tys + mkclasstype(class0) '), class = `java.lang.Object' .class, is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2)

Rule argument

[fma-arg: has_classtype(ty0)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (has_classtype(ty0))]]