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Proof step 29 from proof contains-subspec-better (previous step)

type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), contains(str0, ty, ty0), type∃(str0, ty0), type∃(str, ty0), type∃(str0, ty), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty0 ≤ ty2, is_arraytype(ty1) → ty0 ≤ ty1 .type, ∀ ty0, str0, str, ty, tys0. # tys0 < # [] → ( 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) ⊦ ∃ 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), type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type))

User applied rule cut formula

And obtained the following new goals

Proof step 26:
type∃(str, ty1), type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), contains(str0, ty, ty0), type∃(str0, ty0), type∃(str, ty0), type∃(str0, ty), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty0 ≤ ty2, is_arraytype(ty1) → ty0 ≤ ty1 .type, ∀ ty0, str0, str, ty, tys0. # tys0 < # [] → ( 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) ⊦ ∃ 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), type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type))
Proof step 28:
type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), contains(str0, ty, ty0), type∃(str0, ty0), type∃(str, ty0), type∃(str0, ty), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty0 ≤ ty2, is_arraytype(ty1) → ty0 ≤ ty1 .type, ∀ ty0, str0, str, ty, tys0. # tys0 < # [] → ( 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) ⊦ type∃(str, ty1), ∃ 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), type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type))

Rule argument

[fma-arg: type∃(str, ty1)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (type∃(str, ty1))]]