Commit ee20b2ae by Samuel Ben Hamou

### Fin de la preuve de la loi de De Morgan.

parent 506d1dde
 ... ... @@ -940,7 +940,7 @@ Proof. * apply in_eq. Qed. Lemma Weakening f1 Γ f2 lg : Pr lg (Γ ⊢ f1) -> Pr lg (f2::Γ ⊢ f1). Lemma Weakening Γ f2 lg : forall f1, Pr lg (Γ ⊢ f1) -> Pr lg (f2::Γ ⊢ f1). Admitted. Lemma RAA f1 Γ : Pr Classic (Γ ⊢ ~~f1) -> Pr Classic (Γ ⊢ f1). ... ... @@ -960,16 +960,20 @@ Proof. apply R_Not_e with (A := (~f1 /\ f2)%form). + apply RAA with (f1 := (~f1 /\ f2)%form). apply R_Not_i. apply R_Not_e with (A := (~~f1\/~f2)%form). apply R_Not_e with (A := (f1\/~f2)%form). - apply R_Or_i1. apply RAA. apply R_Not_i. apply R_Not_e with (A := (~~f1\/~f2)%form). apply R_Not_e with (A := (f1\/~f2)%form). * apply R_Or_i2. apply R_Not_i. apply R_Not_e with (A := (~f1 /\ f2)%form). ++ apply R_And_i. -- apply R_Ax. apply in_cons. apply in_eq. -- apply R_Ax. apply in_eq. ++ apply R_Ax. apply in_cons. apply in_cons. apply in_eq. * * apply R_Ax. apply in_cons. apply in_cons. apply in_eq. - apply R_Ax. apply in_cons. apply in_eq. + apply Weakening. exact H. Qed. Lemma ExcludedMiddle f1 : Provable Classic ([] ⊢ f1 \/ ~f1). Proof. ... ...
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