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Proof step 170 from proof same-subclasses-01 (previous step)

same-subclasses-contains(class, str, str0), tdname+∃(str0, class), ty ≤ mkclasstype(class), type∃(str0, ty), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ fs ' ∈ instfields(ty .class) ∧ ty0 ≤ fs .type, is_arraytype(ty) → ty0 ≤ ty .type, ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ tdname+∃(str, class0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 169:
fs = mkfs(class1, ty1, fieldvar), same-subclasses-contains(class, str, str0), tdname+∃(str0, class), ty ≤ mkclasstype(class), type∃(str0, ty), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ fs ' ∈ instfields(ty .class) ∧ ty0 ≤ ty1, is_arraytype(ty) → ty0 ≤ ty .type, ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ tdname+∃(str, class0)

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class1, ty1, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class1, ty1, fieldvar)]]