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Proof step 216 from proof contains-subspec-better (previous step)

contains(str0, ty ' + tys + ty0 '), type∃(str, ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ ty ∈ tys, dups(tys), contains(str, ty, ty0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ type∃(str, ty) → ¬ contains(str, ty ' + tys)
Proof step 215:
¬ ¬ type∃(str0, ty), contains(str0, ty ' + tys + ty0 '), type∃(str, ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ ty ∈ tys, dups(tys), contains(str, ty, ty0)

Rule argument

[crewrite-arg: contains-typeex , F , [tys, ty, str] → [tys + ty0 ', ty, str0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (tys + ty0 ', ty, str0)]]