This question is a proof/logic-based question and it is done with a program called lean which checks to see if you proved it correctly. I have done the first one in lean, but Im not sure how to do the others if someone could help me it would be greatly appreciated. (note: The answer should be in lean format like the first problem)

variables A B C D : Prop

1. example : A (A B) B :=

assume h: A (A B),

have a : A, from and.left h,

have f: A B, from and.right h,

have b: B, from f a,

show B, from b

2. example : A ( A B) :=

3. example : (A B) (A B) :=

4. example (h : A B) (i : A C) (j : B D) : C D :=

5. example (h : A B) : (A B) :=