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Proof step 39 from proof same-subclasses-01 (previous step)

same-subclasses-contains(class, str, str0), type∃(str0, mkclasstype(class)) ∧ is_reftype(mkclasstype(class)) ∧ (∃ ty1. ty1 ≤ mkclasstype(class) ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ mkclasstype(class0) ≤ fs .type)) ∧ (is_arraytype(ty1) → mkclasstype(class0) ≤ ty1 .type) ∧ type∃(str0, mkclasstype(class0))), ∀ class0, str0, str, class, tys0. # tys0 < # [] → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ tdname+∃(str, class0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
same-subclasses-contains(class, str, str0), tdname+∃(str0, class), ty ≤ mkclasstype(class), type∃(str0, ty), tdname+∃(str0, class0), is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ fs ' ∈ instfields(ty .class) ∧ is_classtype(fs .type) ∧ class0 ≤ fs .type .class, is_arraytype(ty) → is_classtype(ty .type) ∧ class0 ≤ ty .type .class, ∀ class0, str0, str, class, tys0. # tys0 < # [] → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ tdname+∃(str, class0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class) ≤ ty ↔ is_classtype(ty) ∧ class ≤ ty .class], [CSIMPSEQ : ⊦ is_reftype(mkclasstype(class))], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)])]]