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Proof step 174 from proof same-subclasses-01 (previous step)

contains(str0, mkclasstype(class) ' + 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ tys ≠ [] → ( contains(str, ty ' + tys) ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ tys .first ≤ fs .type)) ∧ (is_arraytype(ty1) → tys .first ≤ ty1 .type) ∧ contains(str, tys)))
Proof step 173:
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)

Rule argument

[crewrite-arg: contains-rec-01 , F , [tys, ty, str] → [tys + mkclasstype(class0) ', mkclasstype(class), str0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ tys + tys0 ≠ [] ↔ tys = [] ∧ tys0 = []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])], [EXTRATERMS : (tys + mkclasstype(class0) ', mkclasstype(class), str0)]]