From df3a49a18c5b01984000df9244ecea9c275b30cd Mon Sep 17 00:00:00 2001 From: Guillaume Melquiond Date: Mon, 7 Dec 2015 10:52:14 +0100 Subject: Fix some typos. --- theories/Numbers/Integer/Abstract/ZDivEucl.v | 2 +- theories/Numbers/Integer/Abstract/ZDivFloor.v | 2 +- theories/Numbers/Integer/Abstract/ZDivTrunc.v | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) (limited to 'theories/Numbers/Integer') diff --git a/theories/Numbers/Integer/Abstract/ZDivEucl.v b/theories/Numbers/Integer/Abstract/ZDivEucl.v index d0df8fb4a7..ab73ebfe1d 100644 --- a/theories/Numbers/Integer/Abstract/ZDivEucl.v +++ b/theories/Numbers/Integer/Abstract/ZDivEucl.v @@ -391,7 +391,7 @@ rewrite <- (add_0_r (b*(a/b))) at 2. apply add_cancel_l. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, 0 a < b*q -> a/b < q. diff --git a/theories/Numbers/Integer/Abstract/ZDivFloor.v b/theories/Numbers/Integer/Abstract/ZDivFloor.v index d5f3f4ada7..c8260e516f 100644 --- a/theories/Numbers/Integer/Abstract/ZDivFloor.v +++ b/theories/Numbers/Integer/Abstract/ZDivFloor.v @@ -436,7 +436,7 @@ rewrite <- (add_0_r (b*(a/b))) at 2. apply add_cancel_l. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, 0 a < b*q -> a/b < q. diff --git a/theories/Numbers/Integer/Abstract/ZDivTrunc.v b/theories/Numbers/Integer/Abstract/ZDivTrunc.v index de2e99ec3a..464fe354b8 100644 --- a/theories/Numbers/Integer/Abstract/ZDivTrunc.v +++ b/theories/Numbers/Integer/Abstract/ZDivTrunc.v @@ -404,7 +404,7 @@ Proof. intros. rewrite rem_eq by order. rewrite sub_move_r; nzsimpl; tauto. Qed. -(** Some additionnal inequalities about quot. *) +(** Some additional inequalities about quot. *) Theorem quot_lt_upper_bound: forall a b q, 0<=a -> 0 a < b*q -> a÷b < q. -- cgit v1.2.3 From 86f5c0cbfa64c5d0949365369529c5b607878ef8 Mon Sep 17 00:00:00 2001 From: Maxime Dénès Date: Wed, 20 Jan 2016 17:25:10 +0100 Subject: Update copyright headers. --- theories/Numbers/Integer/Abstract/ZAdd.v | 2 +- theories/Numbers/Integer/Abstract/ZAddOrder.v | 2 +- theories/Numbers/Integer/Abstract/ZAxioms.v | 2 +- theories/Numbers/Integer/Abstract/ZBase.v | 2 +- theories/Numbers/Integer/Abstract/ZBits.v | 2 +- theories/Numbers/Integer/Abstract/ZDivEucl.v | 2 +- theories/Numbers/Integer/Abstract/ZDivFloor.v | 2 +- theories/Numbers/Integer/Abstract/ZDivTrunc.v | 2 +- theories/Numbers/Integer/Abstract/ZGcd.v | 2 +- theories/Numbers/Integer/Abstract/ZLcm.v | 2 +- theories/Numbers/Integer/Abstract/ZLt.v | 2 +- theories/Numbers/Integer/Abstract/ZMaxMin.v | 2 +- theories/Numbers/Integer/Abstract/ZMul.v | 2 +- theories/Numbers/Integer/Abstract/ZMulOrder.v | 2 +- theories/Numbers/Integer/Abstract/ZParity.v | 2 +- theories/Numbers/Integer/Abstract/ZPow.v | 2 +- theories/Numbers/Integer/Abstract/ZProperties.v | 2 +- theories/Numbers/Integer/Abstract/ZSgnAbs.v | 2 +- theories/Numbers/Integer/BigZ/BigZ.v | 2 +- theories/Numbers/Integer/BigZ/ZMake.v | 2 +- theories/Numbers/Integer/Binary/ZBinary.v | 2 +- theories/Numbers/Integer/NatPairs/ZNatPairs.v | 2 +- theories/Numbers/Integer/SpecViaZ/ZSig.v | 2 +- theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v | 2 +- 24 files changed, 24 insertions(+), 24 deletions(-) (limited to 'theories/Numbers/Integer') diff --git a/theories/Numbers/Integer/Abstract/ZAdd.v b/theories/Numbers/Integer/Abstract/ZAdd.v index ec8801c4e8..f7fdc17950 100644 --- a/theories/Numbers/Integer/Abstract/ZAdd.v +++ b/theories/Numbers/Integer/Abstract/ZAdd.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* isBigNcst t | BigZ.Neg ?t => isBigNcst t - | BigZ.zero => constr:true - | BigZ.one => constr:true - | BigZ.two => constr:true - | BigZ.minus_one => constr:true - | _ => constr:false + | BigZ.zero => constr:(true) + | BigZ.one => constr:(true) + | BigZ.two => constr:(true) + | BigZ.minus_one => constr:(true) + | _ => constr:(false) end. Ltac BigZcst t := match isBigZcst t with - | true => constr:t - | false => constr:NotConstant + | true => constr:(t) + | false => constr:(NotConstant) end. Ltac BigZ_to_N t := match t with | BigZ.Pos ?t => BigN_to_N t - | BigZ.zero => constr:0%N - | BigZ.one => constr:1%N - | BigZ.two => constr:2%N - | _ => constr:NotConstant + | BigZ.zero => constr:(0%N) + | BigZ.one => constr:(1%N) + | BigZ.two => constr:(2%N) + | _ => constr:(NotConstant) end. (** Registration for the "ring" tactic *) -- cgit v1.2.3