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Proof step 68 from proof same-subclasses-forward (previous step)

type∃(str0, ty), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty3), is_reftype(ty), type∃(str0, ty), type∃(str0, ty1), type∃(str0, ty3), ty1 ≤ ty, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ class0. contains(str0, mkclasstype(ty .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ same-subclasses(ty3 .jtelemtype .class, str, str0) ∧ (contains(str0, ty3 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0)), ∃ ty0. ty0 ≤ ty ∧ type∃(str0, ty0) ∧ (is_classtype(ty0) → ¬ interface∃(str0, ty0 .class) ∧ (∃ fs. fs ' ∈ instfields(ty0 .class) ∧ ty3 ≤ fs .type)) ∧ (is_arraytype(ty0) → ty3 ≤ ty0 .type), ∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, ty3)

User applied rule exists right

And obtained the following new goals

Proof step 67:
type∃(str0, ty), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty3), is_reftype(ty), type∃(str0, ty), type∃(str0, ty1), type∃(str0, ty3), ty1 ≤ ty, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ class0. contains(str0, mkclasstype(ty .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ same-subclasses(ty3 .jtelemtype .class, str, str0) ∧ (contains(str0, ty3 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0)), ty1 ≤ ty ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty3 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty3 ≤ ty1 .type), ∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, ty3)

Rule argument

[EXRARG : pos: right 2, [extquanttermlist: (ty1)abort:F, discard:T, computed:T]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty1)]]