diff -r b698d0b243dc -r fe9504ba63d5 src/HOL/Ring_and_Field.thy --- a/src/HOL/Ring_and_Field.thy Fri May 21 21:15:45 2004 +0200 +++ b/src/HOL/Ring_and_Field.thy Fri May 21 21:16:51 2004 +0200 @@ -1,9 +1,6 @@ (* Title: HOL/Ring_and_Field.thy ID: $Id$ - Author: Gertrud Bauer and Markus Wenzel, TU Muenchen - Lawrence C Paulson, University of Cambridge - Revised and splitted into Ring_and_Field.thy and Group.thy - by Steven Obua, TU Muenchen, in May 2004 + Author: Gertrud Bauer, Steven Obua, Lawrence C Paulson and Markus Wenzel License: GPL (GNU GENERAL PUBLIC LICENSE) *) @@ -19,7 +16,7 @@ \end{itemize} Most of the used notions can also be looked up in \begin{itemize} - \item \emph{www.mathworld.com} by Eric Weisstein et. al. + \item \url{http://www.mathworld.com} by Eric Weisstein et. al. \item \emph{Algebra I} by van der Waerden, Springer. \end{itemize} *} @@ -416,18 +413,6 @@ subsection{*More Monotonicity*} -lemma mult_left_mono_neg: - "[|b \ a; c \ 0|] ==> c * a \ c * (b::'a::pordered_ring)" -apply (drule mult_left_mono [of _ _ "-c"]) -apply (simp_all add: minus_mult_left [symmetric]) -done - -lemma mult_right_mono_neg: - "[|b \ a; c \ 0|] ==> a * c \ b * (c::'a::pordered_ring)" -apply (drule mult_right_mono [of _ _ "-c"]) -apply (simp_all add: minus_mult_right [symmetric]) -done - text{*Strict monotonicity in both arguments*} lemma mult_strict_mono: "[|ac|] ==> a * c < b * (d::'a::ordered_semiring_strict)" @@ -543,7 +528,7 @@ add_diff_eq diff_add_eq diff_diff_eq diff_diff_eq2 diff_eq_eq eq_diff_eq -thm ring_eq_simps + subsection {* Fields *} lemma right_inverse [simp]: