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Proof step 9 from proof same-subclasses-subclass (previous step)

class0 ≤ class, same-subclasses(class, str, str0) ⊦ (class∃(str0, class1) ∧ class1 ≤ class0 → class∃(str, class1)) ∧ (interface∃(str0, class2) ∧ class2 ≤ class0 → interface∃(str, class2))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 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 8:
class0 ≤ class, (∀ class0. class∃(str0, class0) ∧ class0 ≤ class → class∃(str, class0)) ∧ (∀ class0. interface∃(str0, class0) ∧ class0 ≤ class → interface∃(str, class0)) ⊦ (class∃(str0, class1) ∧ class1 ≤ class0 → class∃(str, class1)) ∧ (interface∃(str0, class2) ∧ class2 ≤ class0 → interface∃(str, class2))

Rule argument

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

Additional information

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