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Proof step 92 from proof contains-subspec-better (previous step)

contains(str0, (ty3 ' + tys1) + ty0 '), type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty), type∃(str0, ty0), contains(str0, ty, ty0), type∃(str, ty3), type∃(str0, ty3), type∃(str, ty0), type∃(str0, ty), contains(str, ty3, ty0), has_classtype(ty1), ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0), is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, str0, str, ty, tys0. # tys0 < # (ty3 + tys1) → ( 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 = ty3, ty ∈ tys1, ty3 ∈ tys1, dups(tys1), type∃(str, ty1), is_classtype(ty1), ∃ ty4. ty4 ≤ ty ∧ type∃(str, ty4) ∧ (is_classtype(ty4) → ¬ interface∃(str, ty4 .class) ∧ (∃ fs. fs ' ∈ instfields(ty4 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty4) → ty0 ≤ ty4 .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ ¬ is_reftype(ty) → (ty ≤ ty0 ↔ ty = ty0)
Proof step 91:
¬ ¬ is_reftype(ty1), contains(str0, (ty3 ' + tys1) + ty0 '), type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty), type∃(str0, ty0), contains(str0, ty, ty0), type∃(str, ty3), type∃(str0, ty3), type∃(str, ty0), type∃(str0, ty), contains(str, ty3, ty0), has_classtype(ty1), ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0), is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, str0, str, ty, tys0. # tys0 < # (ty3 + tys1) → ( 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 = ty3, ty ∈ tys1, ty3 ∈ tys1, dups(tys1), type∃(str, ty1), is_classtype(ty1), ∃ ty4. ty4 ≤ ty ∧ type∃(str, ty4) ∧ (is_classtype(ty4) → ¬ interface∃(str, ty4 .class) ∧ (∃ fs. fs ' ∈ instfields(ty4 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty4) → ty0 ≤ ty4 .type)

Rule argument

[speclemmaarg: ,¬ is_reftype(ty) → (ty ≤ ty0 ↔ ty = ty0) ,[ty0, ty] → [ty, ty1] ,F ,typefuns , ,le-noreftype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_classtype(ty) → ( is_reftype(ty) ↔ is_arraytype(ty))], [CSIMPSEQ : ⊦ is_arraytype(ty) → ty .jtelemtype = ty .type .jtelemtype], [CSIMPSEQ : ⊦ ¬ is_reftype(ty) → ¬ has_classtype(ty)])], [EXTRATERMS : (ty, ty1)]]