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Proof step 16 from proof contains-predefined (previous step)

contains(str, mkclasstype(class), ty), is_predefined_class(class), ∀ class0. tdname∃(str, class0) ∧ class0 ≤ class → is_predefined_class(class0) ⊦ class = `java.lang.Object' .class

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 15:
type∃(str, mkclasstype(class)) ∧ is_reftype(mkclasstype(class)) ∧ ( (∃ ty1. ty1 ≤ mkclasstype(class) ∧ type∃(str, ty1) ∧ type∃(str, ty) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty ≤ fs .type)) ∧ (is_arraytype(ty1) → ty ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ mkclasstype(class) ∧ 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, ty))), is_predefined_class(class), ∀ class0. tdname∃(str, class0) ∧ class0 ≤ class → is_predefined_class(class0) ⊦ class = `java.lang.Object' .class

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: contains-type-rec antecedent: succedent: 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))) substlist: [ty0, ty, str] → [ty, mkclasstype(class), str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty, mkclasstype(class), str)]]