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Proof step 22 from proof contains-subex (conclusion)

⊦ (∀ ty1. contains(str0, ty, ty1) → type∃(str, ty1)) ↔ (∀ class1. contains(str0, ty, mkclasstype(class1)) → tdname+∃(str, class1))

User applied rule case distinction

And obtained the following new goals

Proof step 2:
∀ ty1. contains(str0, ty, ty1) → type∃(str, ty1) ⊦ ∀ class1. contains(str0, ty, mkclasstype(class1)) → tdname+∃(str, class1)
Proof step 21:
∀ class1. contains(str0, ty, mkclasstype(class1)) → tdname+∃(str, class1) ⊦ ∀ ty1. contains(str0, ty, ty1) → type∃(str, ty1)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]