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Proof step 12 from proof same-subclasses-trans (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 7:
∀ class0. class∃(str0, class0) ∧ class0 ≤ class → class∃(str, class0), ∀ class0. interface∃(str0, class0) ∧ class0 ≤ class → interface∃(str, class0), ∀ class0. interface∃(str1, class0) ∧ class0 ≤ class → interface∃(str0, class0), ∀ class0. class∃(str1, class0) ∧ class0 ≤ class → class∃(str0, class0) ⊦ class∃(str1, class0) ∧ class0 ≤ class → class∃(str, class0)
Proof step 11:
∀ class0. class∃(str0, class0) ∧ class0 ≤ class → class∃(str, class0), ∀ class0. interface∃(str0, class0) ∧ class0 ≤ class → interface∃(str, class0), ∀ class0. interface∃(str1, class0) ∧ class0 ≤ class → interface∃(str0, class0), ∀ class0. class∃(str1, class0) ∧ class0 ≤ class → class∃(str0, class0) ⊦ interface∃(str1, class1) ∧ class1 ≤ class → interface∃(str, class1)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]