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Proof step 9 from proof same-subclasses-contains-trans (previous step)

contains(str1, mkclasstype(class), mkclasstype(class0)), same-subclasses(class, str, str0), same-subclasses-contains(class, str0, str1), same-subclasses(class, str, str1), contains(str0, mkclasstype(class), mkclasstype(class0)), same-subclasses(class0, str, str0) ⊦ same-subclasses(class0, str, str1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ same-subclasses-contains(class, str, str0) ↔ same-subclasses(class, str, str0) ∧ (∀ class0. contains(str0, mkclasstype(class), mkclasstype(class0)) → same-subclasses(class0, str, str0))
Proof step 8:
contains(str1, mkclasstype(class), mkclasstype(class0)), same-subclasses(class, str, str0), same-subclasses(class, str0, str1) ∧ (∀ class0. contains(str1, mkclasstype(class), mkclasstype(class0)) → same-subclasses(class0, str0, str1)), same-subclasses(class, str, str1), contains(str0, mkclasstype(class), mkclasstype(class0)), same-subclasses(class0, str, str0) ⊦ same-subclasses(class0, str, str1)

Rule argument

[crewrite-arg: same-subclasses-all-def , F , [str0, str, class] → [str1, str0, class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str1, str0, class)]]