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Proof step 55 from proof contains-subspec (previous step)

type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str0, ty), has_classtype(ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), level⊆(str0, str), type∃(str, ty), contains(str0, tys + ty0 '), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ tys .first ≤ ty2, is_arraytype(ty1) → tys .first ≤ ty1 .type, ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ level⊆(str0, str) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys = [], contains(str, ty, ty0), dups(tys), ty ∈ tys

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 54:
tys = ty3 + tys1, type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str0, ty), has_classtype(ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), level⊆(str0, str), type∃(str, ty), contains(str0, tys + ty0 '), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ level⊆(str0, str) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys = [], contains(str, ty, ty0), dups(tys), ty ∈ tys

Rule argument

[speclemmaarg: tys ≠ [] ,ty = tys .first ∧ tys0 = tys .rest ↔ tys = ty + tys0 ,[tys, ty, tys0] → [tys, ty3, tys1] ,T ,list-data ,javatypes ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : tys ≠ [] ⊦ ty = tys .first ∧ tys0 = tys .rest ↔ tys = ty + tys0])], [EXTRATERMS : (tys, ty3, tys1)]]