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Proof step 123 from proof contains-subspec-better (previous step)

type∃(str0, ty), type∃(str, ty0), type∃(str0, ty3), type∃(str, ty3), contains(str0, ty, ty0), type∃(str0, ty0), has_classtype(ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), contains(str0, (ty3 ' + tys1) + ty0 '), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ 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, contains(str, ty, ty0), dups(tys1), ty3 ∈ tys1, ty ∈ tys1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ contains(str, ty, ty0) ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ ( (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ type∃(str, ty0) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str, ty2, ty0)))
Proof step 122:
type∃(str0, ty), type∃(str, ty0), type∃(str0, ty3), type∃(str, ty3), contains(str0, ty, ty0), type∃(str0, ty0), has_classtype(ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), contains(str0, (ty3 ' + tys1) + ty0 '), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ 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, type∃(str, ty) ∧ is_reftype(ty) ∧ ( (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ type∃(str, ty0) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str, ty2, ty0))), dups(tys1), ty3 ∈ tys1, ty ∈ tys1

Rule argument

[crewrite-arg: contains-type-rec, F, [ty0, ty, str] → [ty0, ty, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty0, ty, str)]]