Set: pp::colors Set: pp::unicode Assumed: f Proved: T1 Proved: T2 Theorem T1 (a b c : ℤ) (H1 : a = b) (H2 : a = c) : (f (f a a) b) = (f (f b c) a) := Congr (Congr (Refl f) (Congr (Congr (Refl f) H1) H2)) (Symm H1) Theorem T2 (a b c : ℤ) (H1 : a = b) (H2 : a = c) : (f (f a c)) = (f (f b a)) := Congr (Refl f) (Congr (Congr (Refl f) H1) (Symm H2))