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Proof step 173 from proof same-subclasses-01 (previous step)

tys + mkclasstype(class0) ' ≠ [], 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) ∧ (tys + mkclasstype(class0) ') .first ≤ fs .type)) ∧ (is_arraytype(ty1) → (tys + mkclasstype(class0) ') .first ≤ ty1 .type) ∧ contains(str0, tys + mkclasstype(class0) ')), same-subclasses-contains(class, str, str0), ∀ class0, str0, str, class, tys0. # tys0 < # tys → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ tys = [], tdname+∃(str, class0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 172:
ty ≤ mkclasstype(class), type∃(str0, ty), contains(str0, tys + mkclasstype(class0) '), same-subclasses-contains(class, str, str0), tdname+∃(str0, class), is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ fs ' ∈ instfields(ty .class) ∧ tys .first ≤ fs .type, is_arraytype(ty) → tys .first ≤ ty .type, ∀ class0, str0, str, class, tys0. # tys0 < # tys → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ tys = [], tdname+∃(str, class0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ tys ≠ [] → (tys + tys0) .first = tys .first], [CSIMPSEQ : ⊦ is_reftype(mkclasstype(class))], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ tys + ty ' ≠ []])]]