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- (* exercise 3.5 from Coq Art *)
- Section section_for_cut_example.
- Variables P Q R T : Prop.
- Hypotheses (H : P -> Q)
- (H0 : Q -> R)
- (H1 : (P -> R) -> T -> Q)
- (H2 : (P -> R) -> T).
- Theorem cut_example : Q.
- Proof.
- cut (P -> R).
- intro H3.
- apply H1; [assumption | apply H2; assumption].
- intro H3; apply H0; apply H; assumption.
- Qed.
- Theorem cut_example_without_cut : Q.
- Proof.
- apply H1.
- intro H3; apply H0; apply H; assumption.
- apply H2.
- intro H3; apply H0; apply H; assumption.
- Qed.
- End section_for_cut_example.
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