Commit bd9241dc by Samuel Ben Hamou

### Mini modifs Peano (retours à la ligne pour plus de lisibilité)

parent 73d69bcc
 ... ... @@ -99,7 +99,9 @@ Definition PeanoTheory := Import PeanoAx. Lemma Symmetry : forall logic A B Γ, BClosed A -> In ax2 Γ -> Pr logic (Γ ⊢ A = B) -> Pr logic (Γ ⊢ B = A). Lemma Symmetry : forall logic A B Γ, BClosed A -> In ax2 Γ -> Pr logic (Γ ⊢ A = B) -> Pr logic (Γ ⊢ B = A). Proof. intros. apply R_Imp_e with (A := A = B); [ | assumption ]. ... ... @@ -115,7 +117,9 @@ Proof. exact AX2. Qed. Lemma Transitivity : forall logic A B C Γ, BClosed A -> BClosed B -> In ax3 Γ -> Pr logic (Γ ⊢ A = B) -> Pr logic (Γ ⊢ B = C) -> Pr logic (Γ ⊢ A = C). Lemma Transitivity : forall logic A B C Γ, BClosed A -> BClosed B -> In ax3 Γ -> Pr logic (Γ ⊢ A = B) -> Pr logic (Γ ⊢ B = C) -> Pr logic (Γ ⊢ A = C). Proof. intros. apply R_Imp_e with (A := A = B /\ B = C); [ | apply R_And_i; assumption ]. ... ... @@ -138,7 +142,9 @@ Proof. assumption. Qed. Lemma Hereditarity : forall logic A B Γ, BClosed A -> In ax4 Γ -> Pr logic (Γ ⊢ A = B) -> Pr logic (Γ ⊢ Succ A = Succ B). Lemma Hereditarity : forall logic A B Γ, BClosed A -> In ax4 Γ -> Pr logic (Γ ⊢ A = B) -> Pr logic (Γ ⊢ Succ A = Succ B). Proof. intros. apply R_Imp_e with (A := A = B); [ | assumption ]. ... ... @@ -155,7 +161,9 @@ Proof. assumption. Qed. Lemma AntiHereditarity : forall logic A B Γ, BClosed A -> In ax13 Γ -> Pr logic (Γ ⊢ Succ A = Succ B) -> Pr logic (Γ ⊢ A = B). Lemma AntiHereditarity : forall logic A B Γ, BClosed A -> In ax13 Γ -> Pr logic (Γ ⊢ Succ A = Succ B) -> Pr logic (Γ ⊢ A = B). Proof. intros. apply R_Imp_e with (A := Succ A = Succ B); [ | assumption ]. ... ...
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