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Proof step 14 from proof same-subclasses-trans (previous step)

same-subclasses(class, str0, str1), ∀ class0. interface∃(str0, class0) ∧ class0 ≤ class → interface∃(str, class0), ∀ class0. class∃(str0, class0) ∧ class0 ≤ class → class∃(str, class0) ⊦ (class∃(str1, class0) ∧ class0 ≤ class → class∃(str, class0)) ∧ (interface∃(str1, class1) ∧ class1 ≤ class → interface∃(str, class1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ same-subclasses(class, str, str0) ↔ (∀ class0. class∃(str0, class0) ∧ class0 ≤ class → class∃(str, class0)) ∧ (∀ class0. interface∃(str0, class0) ∧ class0 ≤ class → interface∃(str, class0))
Proof step 13:
(∀ class0. class∃(str1, class0) ∧ class0 ≤ class → class∃(str0, class0)) ∧ (∀ class0. interface∃(str1, class0) ∧ class0 ≤ class → interface∃(str0, class0)), ∀ class0. interface∃(str0, class0) ∧ class0 ≤ class → interface∃(str, class0), ∀ class0. class∃(str0, class0) ∧ class0 ≤ class → class∃(str, class0) ⊦ (class∃(str1, class0) ∧ class0 ≤ class → class∃(str, class0)) ∧ (interface∃(str1, class1) ∧ class1 ≤ class → interface∃(str, class1))

Rule argument

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

Additional information

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