diff options
Diffstat (limited to 'theories/Numbers/Integer/Abstract')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZBits.v | 6 | ||||
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivEucl.v | 3 |
2 files changed, 5 insertions, 4 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZBits.v b/theories/Numbers/Integer/Abstract/ZBits.v index 2da4452819..4aabda77ee 100644 --- a/theories/Numbers/Integer/Abstract/ZBits.v +++ b/theories/Numbers/Integer/Abstract/ZBits.v @@ -80,7 +80,7 @@ Proof. now apply testbit_even_succ. Qed. -(** Alternative caracterisations of [testbit] *) +(** Alternative characterisations of [testbit] *) (** This concise equation could have been taken as specification for testbit in the interface, but it would have been hard to @@ -102,10 +102,10 @@ Proof. left. destruct b; split; simpl; order'. Qed. -(** This caracterisation that uses only basic operations and +(** This characterisation that uses only basic operations and power was initially taken as specification for testbit. We describe [a] as having a low part and a high part, with - the corresponding bit in the middle. This caracterisation + the corresponding bit in the middle. This characterisation is moderatly complex to implement, but also moderately usable... *) diff --git a/theories/Numbers/Integer/Abstract/ZDivEucl.v b/theories/Numbers/Integer/Abstract/ZDivEucl.v index d7f25a6613..a70ecd19d8 100644 --- a/theories/Numbers/Integer/Abstract/ZDivEucl.v +++ b/theories/Numbers/Integer/Abstract/ZDivEucl.v @@ -13,7 +13,7 @@ Require Import ZAxioms ZMulOrder ZSgnAbs NZDiv. (** * Euclidean Division for integers, Euclid convention We use here the "usual" formulation of the Euclid Theorem - [forall a b, b<>0 -> exists b q, a = b*q+r /\ 0 < r < |b| ] + [forall a b, b<>0 -> exists r q, a = b*q+r /\ 0 <= r < |b| ] The outcome of the modulo function is hence always positive. This corresponds to convention "E" in the following paper: @@ -46,6 +46,7 @@ Module ZEuclidProp (** We put notations in a scope, to avoid warnings about redefinitions of notations *) + Declare Scope euclid. Infix "/" := D.div : euclid. Infix "mod" := D.modulo : euclid. Local Open Scope euclid. |