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author | 2002-04-17 11:30:23 +0000 | |
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committer | 2002-04-17 11:30:23 +0000 | |
commit | cc1be0bf512b421336e81099aa6906ca47e4257a (patch) | |
tree | c25fa8ed965729d7a85efa3b3292fdf7f442963d /theories/Num/AddProps.v | |
parent | ebf9aa9f97ef0d49ed1b799c9213f78efad4fec7 (diff) |
Uniformisation (Qed/Save et Implicits Arguments)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2650 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Num/AddProps.v')
-rw-r--r-- | theories/Num/AddProps.v | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/theories/Num/AddProps.v b/theories/Num/AddProps.v index 739ead5e0..cbd8d9e4e 100644 --- a/theories/Num/AddProps.v +++ b/theories/Num/AddProps.v @@ -14,44 +14,44 @@ Require Export EqAxioms. (** Properties of Addition *) Lemma add_x_0 : (x:N)(x+zero)=x. EAuto 3 with num. -Save. +Qed. Hints Resolve add_x_0 : num. Lemma add_x_Sy : (x,y:N)(x+(S y))=(S (x+y)). Intros x y; Apply eq_trans with (S y)+x; EAuto with num. -Save. +Qed. Hints Resolve add_x_Sy : num. Lemma add_x_Sy_swap : (x,y:N)(x+(S y))=((S x)+y). EAuto with num. -Save. +Qed. Hints Resolve add_x_Sy_swap : num. Lemma add_Sx_y_swap : (x,y:N)((S x)+y)=(x+(S y)). Auto with num. -Save. +Qed. Hints Resolve add_Sx_y_swap : num. Lemma add_assoc_r : (x,y,z:N)(x+(y+z))=((x+y)+z). Auto with num. -Save. +Qed. Hints Resolve add_assoc_r : num. Lemma add_x_y_z_perm : (x,y,z:N)((x+y)+z)=(y+(x+z)). EAuto with num. -Save. +Qed. Hints Resolve add_x_y_z_perm : num. Lemma add_x_one_S : (x:N)(x+one)=(S x). Intros; Apply eq_trans with (x+(S zero)); EAuto with num. -Save. +Qed. Hints Resolve add_x_one_S : num. Lemma add_one_x_S : (x:N)(one+x)=(S x). Intros; Apply eq_trans with (x+one); Auto with num. -Save. +Qed. Hints Resolve add_one_x_S : num. |