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Proof step 154 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, type∃(str0, ty0 .jtelemtype), is_reftype(ty0 .jtelemtype), ty ≤ ty0 .jtelemtype, type∃(str0, ty), contains(str0, tys + mkclasstype(class0) '), is_arraytype(ty) → (tys + mkclasstype(class0) ') .first ≤ ty .type, is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ mkfs(class3, ty2, fieldvar0) ' ∈ instfields(ty .class) ∧ (tys + mkclasstype(class0) ') .first ≤ ty2, ∀ 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, has_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2), same-subclasses-contains(ty0 .jtelemtype .class, str, str0) ∧ contains(str0, mkclasstype(ty0 .jtelemtype .class) ' + tys + mkclasstype(class0) ')

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 153:
tys + mkclasstype(class0) ' = ty3 + tys2 ∧ tys + mkclasstype(class0) ' ≠ [], 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, type∃(str0, ty0 .jtelemtype), is_reftype(ty0 .jtelemtype), ty ≤ ty0 .jtelemtype, type∃(str0, ty), contains(str0, tys + mkclasstype(class0) '), is_arraytype(ty) → ty3 ≤ ty .type, is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ mkfs(class3, ty2, fieldvar0) ' ∈ instfields(ty .class) ∧ ty3 ≤ ty2, ∀ 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, has_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2), same-subclasses-contains(ty0 .jtelemtype .class, str, str0) ∧ contains(str0, mkclasstype(ty0 .jtelemtype .class) ' + tys + mkclasstype(class0) ')

Rule argument

[speclemmaarg: tys ≠ [] ,ty = tys .first ∧ tys0 = tys .rest ↔ tys = ty + tys0 ,[tys, ty, tys0] → [tys + mkclasstype(class0) ', ty3, tys2] ,T ,list-data ,javatypes ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ tys + tys0 ≠ [] ↔ tys = [] ∧ tys0 = []], [CSIMPSEQ : ⊦ ty ' ≠ []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPELIM : tys ≠ [] ⊦ ty = tys .first ∧ tys0 = tys .rest ↔ tys = ty + tys0])], [EXTRATERMS : (tys + mkclasstype(class0) ', ty3, tys2)]]