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Proof step 12 from proof levelsubset-trans (previous step)

∀ class. class∃(str, class) → class∃(str0, class), ∀ class. interface∃(str, class) → interface∃(str0, class), ∀ class. interface∃(str0, class) → interface∃(str1, class), ∀ class. class∃(str0, class) → class∃(str1, class) ⊦ (class∃(str, class) → class∃(str1, class)) ∧ (interface∃(str, class0) → interface∃(str1, class0))

User applied rule case distinction

And obtained the following new goals

Proof step 7:
∀ class. class∃(str, class) → class∃(str0, class), ∀ class. interface∃(str, class) → interface∃(str0, class), ∀ class. interface∃(str0, class) → interface∃(str1, class), ∀ class. class∃(str0, class) → class∃(str1, class) ⊦ class∃(str, class) → class∃(str1, class)
Proof step 11:
∀ class. class∃(str, class) → class∃(str0, class), ∀ class. interface∃(str, class) → interface∃(str0, class), ∀ class. interface∃(str0, class) → interface∃(str1, class), ∀ class. class∃(str0, class) → class∃(str1, class) ⊦ interface∃(str, class0) → interface∃(str1, class0)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]