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Question Proof Logic Based Question Done Program Called Lean Checks See Proved Correctly D Q43906555

This question is a proof/logic-based question and it is donewith a program called lean which checks to see if you proved itcorrectly. I have done the first one in lean, but I’m not sure howto do the others if someone could help me it would be greatlyappreciated. (note: The answer should be in lean format like thefirst 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) :=

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Answer to This question is a proof/logic-based question and it is done with a program called lean which checks to see if you prove…