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Proof step 172 from proof same-subclasses-01 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 171:
tys = ty0 + tys1, ty ≤ mkclasstype(class), type∃(str0, ty), contains(str0, tys + mkclasstype(class0) '), same-subclasses-contains(class, str, str0), tdname+∃(str0, class), 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 < # tys → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ tys = [], tdname+∃(str, class0)

Rule argument

[speclemmaarg: tys ≠ [] ,ty = tys .first ∧ tys0 = tys .rest ↔ tys = ty + tys0 ,[tys, ty, tys0] → [tys, ty0, tys1] ,T ,list-data ,javatypes ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : tys ≠ [] ⊦ ty = tys .first ∧ tys0 = tys .rest ↔ tys = ty + tys0])], [EXTRATERMS : (tys, ty0, tys1)]]