UserGuide.lyx: fix some typographic issues spotted by Mike

[lyx.git] / lib / examples / beamerlyxexample1.lyx

diff --git a/lib/examples/beamerlyxexample1.lyx b/lib/examples/beamerlyxexample1.lyx
index aaff49bcc8ae05a2ba8f7a9854dfa4b7601c20d7..9d51a378bcbba090a36eeb2befa4b16c9d367482 100644 (file)
--- a/lib/examples/beamerlyxexample1.lyx
+++ b/lib/examples/beamerlyxexample1.lyx
@@ -1,7 +1,8 @@
 #LyX 2.2 created this file. For more info see http://www.lyx.org/
-\lyxformat 503
+\lyxformat 508
 \begin_document
 \begin_header
+\save_transient_properties true
 \origin /systemlyxdir/examples/
 \textclass beamer
 \begin_preamble
@@ -261,9 +262,6 @@ Outline
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -364,17 +362,11 @@ Tournaments Consist of Jousts Between Knights
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
 \begin_layout Columns
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -563,9 +555,6 @@ What is a Tournament?
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -612,12 +601,11 @@ In every joust one knight wins.
 \end_deeper
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 4
@@ -630,17 +618,11 @@ Tournaments are Complete Directed Graphs
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
 \begin_layout Columns
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -867,10 +849,6 @@ tournament
  
 \color inherit
 is a
-\color inherit
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -890,12 +868,11 @@ any two different vertices.
 \end_deeper
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 2
@@ -918,9 +895,6 @@ Tournaments Arise Naturally in Different Situations
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -935,9 +909,6 @@ Applications in Ordering Theory
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -952,12 +923,11 @@ The comparison relation may be cyclic, however.
 
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout ExampleBlock
 \begin_inset Argument 2
@@ -970,9 +940,6 @@ Applications in Sociology
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -987,12 +954,11 @@ Reviewers decide for any two candidates whom they prefer.
 
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout ExampleBlock
 \begin_inset Argument 2
@@ -1005,9 +971,6 @@ Applications in Structural Complexity Theory
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -1048,9 +1011,6 @@ status open
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -1187,9 +1147,6 @@ the Approximation Problem
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -1326,9 +1283,6 @@ status open
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -1343,9 +1297,6 @@ t,onlytextwidth
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -1419,9 +1370,6 @@ Example Input
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -1811,9 +1759,6 @@ Example Output
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -2040,9 +1985,6 @@ status open
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -2057,9 +1999,6 @@ Variants of Path Finding Problems
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -2275,9 +2214,6 @@ Logspace Turing Machines
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -2446,12 +2382,11 @@ end{pgfpicture}
 
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 4
@@ -2464,9 +2399,6 @@ Logspace Turing Machines Are Quite Powerful
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -2481,9 +2413,6 @@ Deterministic logspace machines can compute
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -2515,9 +2444,6 @@ Non-deterministic logspace machines can compute
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -2536,12 +2462,11 @@ satisfiability with two literals per clause.
 \end_deeper
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 1
@@ -2574,9 +2499,6 @@ The Complexity Class Hierarchy
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -2965,12 +2887,11 @@ end{pgfpicture}
 
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 4
@@ -2999,9 +2920,6 @@ Limit the Circuit Depth
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3041,9 +2959,6 @@ t
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3066,9 +2981,6 @@ Circuit Class
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3086,9 +2998,6 @@ unbounded fan-in
 \end_deeper
 \begin_layout Examples
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3130,9 +3039,6 @@ Circuit Class
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3150,9 +3056,6 @@ bounded fan-in
 \end_deeper
 \begin_layout Examples
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3201,9 +3104,6 @@ Circuit Class
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3221,9 +3121,6 @@ bounded fan-in
 \end_deeper
 \begin_layout Examples
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3269,9 +3166,6 @@ Are Equally Difficult
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3297,9 +3191,6 @@ Are Equally Difficult
 
 \begin_layout Corollary
 For directed graphs, we can solve
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3365,9 +3256,6 @@ But Not Trivial
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3387,12 +3275,11 @@ But Not Trivial
 \end_layout
 
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}_{\operatorname{path}}$
@@ -3442,9 +3329,6 @@ Definition of the Tournament Reachability Problem
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3466,10 +3350,6 @@ contain all triples
 \end_inset
 
  such that
-\color inherit
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3503,12 +3383,11 @@ there exists a path from
 \end_deeper
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 4
@@ -3521,9 +3400,6 @@ The Tournament Reachability Problem is Very Easy
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3549,9 +3425,6 @@ Implications
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3616,9 +3489,6 @@ the Distance Problem
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3640,10 +3510,6 @@ contain all tuples
 \end_inset
 
  such that 
-\color inherit
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3681,12 +3547,11 @@ the distance of
 \end_deeper
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 4
@@ -3699,9 +3564,6 @@ The Tournament Distance Problem is Hard
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3767,12 +3629,11 @@ in logarithmic space, iff
 
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 4
@@ -3789,9 +3650,6 @@ Proof That
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3822,9 +3680,6 @@ t,onlytextwidth
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3869,9 +3724,6 @@ Reduce
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -3940,12 +3792,11 @@ Query:
 
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Block
 \begin_inset Argument 2
@@ -3968,9 +3819,6 @@ status open
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5126,9 +4974,6 @@ Approximators Compute Paths that Are Nearly As Short As a Shortest Path
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5146,10 +4991,6 @@ approximation scheme for
  
 \color inherit
 gets as input
-\color inherit
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5196,12 +5037,11 @@ a path from
 \end_deeper
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 4
@@ -5218,9 +5058,6 @@ the Tournament Shortest Path Problem
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5302,7 +5139,7 @@ fragile
 \end_inset
 
 .
- \SpecialCharNoPassThru LyX
+ \SpecialChar LyX
  has the FragileFrame layout for this.
 \end_layout
 
@@ -5326,9 +5163,6 @@ Just a frame with a program code listing
 
 \begin_layout FragileFrame
 This is some program code:
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5408,9 +5242,6 @@ Summary
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5425,9 +5256,6 @@ Summary
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5498,12 +5326,11 @@ in tournaments is
 
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Block
 \begin_inset Argument 2
@@ -5516,9 +5343,6 @@ Outlook
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5593,9 +5417,6 @@ For Further Reading
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5828,9 +5649,6 @@ Definition of Independence Number of a Graph
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5865,12 +5683,11 @@ Tournaments have independence number 1.
 
 \end_deeper
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Frame
 \begin_inset Argument 4
@@ -5887,9 +5704,6 @@ Graphs With Bounded Independence Number
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -5930,12 +5744,11 @@ at most
 \end_layout
 
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Theorem
 For each
@@ -5967,12 +5780,11 @@ for approximating the shortest path in graphs with independence number at
 \end_layout
 
 \begin_layout Standard
-
-\begin_inset Separator parbreak
+\begin_inset Separator plain
 \end_inset
 
-\end_layout
 
+\end_layout
 
 \begin_layout Theorem
 For each
@@ -6052,9 +5864,6 @@ Is Party Unknown.
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -6071,9 +5880,6 @@ Is Party Unknown.
 
 \begin_layout Corollary
 For undirected graphs, we can solve
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -6209,9 +6015,6 @@ The Approximation Scheme is Optimal
 \end_inset
 
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper
@@ -6234,9 +6037,6 @@ Suppose there exists an approximation scheme for
 
 \begin_layout Proof
 
-\begin_inset Separator parbreak
-\end_inset
-
 \end_layout
 
 \begin_deeper