Oops

7 files changed, 127 insertions, 123 deletions

diff --git a/graf/n1.lyx b/graf/n1.lyx
index 921c7d8..0f2f84f 100644
--- a/graf/n1.lyx
+++ b/graf/n1.lyx
@@ -209,7 +209,7 @@ Dados un grafo
 \end_inset
 
  y 
-\begin_inset Formula $e:=(i,j)\in E$
+\begin_inset Formula $e\coloneqq (i,j)\in E$
 \end_inset
 
 , 
@@ -346,7 +346,7 @@ G^{\complement}:=(V,E^{\complement}):=(V,\{S\in{\cal P}(V)\mid |S|=2,S\notin E\}
 \end_inset
 
 Un grafo 
-\begin_inset Formula $G':=(V',E')$
+\begin_inset Formula $G'\coloneqq (V',E')$
 \end_inset
 
  es un 
@@ -354,7 +354,7 @@ Un grafo
 subgrafo
 \series default
  de 
-\begin_inset Formula $G:=(V,E)$
+\begin_inset Formula $G\coloneqq (V,E)$
 \end_inset
 
  si 
@@ -404,11 +404,11 @@ inducido
 \end_inset
 
  a 
-\begin_inset Formula $G_{V'}:=(V',E_{V'})$
+\begin_inset Formula $G_{V'}\coloneqq (V',E_{V'})$
 \end_inset
 
 , donde 
-\begin_inset Formula $E_{V'}:=\{S\in E\mid S\subseteq V'\}$
+\begin_inset Formula $E_{V'}\coloneqq \{S\in E\mid S\subseteq V'\}$
 \end_inset
 
 , y 
@@ -462,7 +462,7 @@ independiente
 \end_inset
 
 , 
-\begin_inset Formula $G-v:=G-\{v\}$
+\begin_inset Formula $G-v\coloneqq G-\{v\}$
 \end_inset
 
 , y si 
@@ -470,7 +470,7 @@ independiente
 \end_inset
 
 , 
-\begin_inset Formula $G-e:=G-\{e\}$
+\begin_inset Formula $G-e\coloneqq G-\{e\}$
 \end_inset
 
 .
@@ -504,11 +504,11 @@ maximal
 
 \begin_layout Standard
 Dos grafos 
-\begin_inset Formula $G:=(V,E)$
+\begin_inset Formula $G\coloneqq (V,E)$
 \end_inset
 
  y 
-\begin_inset Formula $G':=(V',E')$
+\begin_inset Formula $G'\coloneqq (V',E')$
 \end_inset
 
  son 
@@ -540,7 +540,7 @@ Grado de un nodo
 
 \begin_layout Standard
 Dado un grafo 
-\begin_inset Formula $G:=(V,E)$
+\begin_inset Formula $G\coloneqq (V,E)$
 \end_inset
 
 , llamamos 
@@ -627,11 +627,11 @@ eje colgante
 \series default
 .
  Llamamos 
-\begin_inset Formula $\delta_{G}:=\min_{v\in V}o(v)$
+\begin_inset Formula $\delta_{G}\coloneqq \min_{v\in V}o(v)$
 \end_inset
 
  y 
-\begin_inset Formula $\Delta_{G}:=\max_{v\in V}o(v)$
+\begin_inset Formula $\Delta_{G}\coloneqq \max_{v\in V}o(v)$
 \end_inset
 
 .
@@ -749,7 +749,7 @@ Teorema de Erdös y Gallai
 :
 \series default
  Una secuencia 
-\begin_inset Formula $S:=(d_{1},\dots,d_{n})$
+\begin_inset Formula $S\coloneqq (d_{1},\dots,d_{n})$
 \end_inset
 
  monótona decreciente de naturales es una secuencia gráfica si y sólo si
@@ -1598,7 +1598,7 @@ status open
 \end_inset
 
 Sea 
-\begin_inset Formula $G:=(\{1,\dots,n\},E)$
+\begin_inset Formula $G\coloneqq (\{1,\dots,n\},E)$
 \end_inset
 
  un grafo con 
@@ -2008,7 +2008,7 @@ Representaciones matriciales
 
 \begin_layout Standard
 Dado un grafo no dirigido 
-\begin_inset Formula $G:=(\{1,\dots,n\},E)$
+\begin_inset Formula $G\coloneqq (\{1,\dots,n\},E)$
 \end_inset
 
 , la 
@@ -2020,7 +2020,7 @@ matriz de adyacencia
 \end_inset
 
  es la matriz 
-\begin_inset Formula $A:=(a_{ij})_{ij}\in{\cal M}_{n}(\mathbb{Z})$
+\begin_inset Formula $A\coloneqq (a_{ij})_{ij}\in{\cal M}_{n}(\mathbb{Z})$
 \end_inset
 
  dada por 
diff --git a/graf/n2.lyx b/graf/n2.lyx
index 9d905d7..dd4d85b 100644
--- a/graf/n2.lyx
+++ b/graf/n2.lyx
@@ -513,7 +513,7 @@ Recorrido de componentes conexas
 
 \begin_layout Standard
 Sean 
-\begin_inset Formula $G:=(V,E)$
+\begin_inset Formula $G\coloneqq (V,E)$
 \end_inset
 
  un grafo de orden 
@@ -1224,7 +1224,7 @@ Demostración:
 \end_inset
 
 , 
-\begin_inset Formula $Y:=[V_{1},V\setminus V_{1}]$
+\begin_inset Formula $Y\coloneqq [V_{1},V\setminus V_{1}]$
 \end_inset
 
  es un corte contenido estrictamente en 
@@ -1336,7 +1336,7 @@ Si
 \end_inset
 
  Sean 
-\begin_inset Formula $[V_{1},V_{2}]:=\{e\}$
+\begin_inset Formula $[V_{1},V_{2}]\coloneqq \{e\}$
 \end_inset
 
 , 
@@ -1653,7 +1653,7 @@ Demostración:
 \end_inset
 
  y 
-\begin_inset Formula $q:=|V_{1}|$
+\begin_inset Formula $q\coloneqq |V_{1}|$
 \end_inset
 
 .
@@ -2013,7 +2013,7 @@ Si
 
 .
  Si 
-\begin_inset Formula $e:=(u,v)\in E$
+\begin_inset Formula $e\coloneqq (u,v)\in E$
 \end_inset
 
 , como 
@@ -2137,15 +2137,15 @@ grafo en línea
 \end_inset
 
  es 
-\begin_inset Formula $L(G):=(V^{L},E^{L})$
+\begin_inset Formula $L(G)\coloneqq (V^{L},E^{L})$
 \end_inset
 
  dado por 
-\begin_inset Formula $V^{L}:=E$
+\begin_inset Formula $V^{L}\coloneqq E$
 \end_inset
 
  y 
-\begin_inset Formula $E^{L}:=\{(e,f)\mid e\neq f,e\cap f\neq\emptyset\}$
+\begin_inset Formula $E^{L}\coloneqq \{(e,f)\mid e\neq f,e\cap f\neq\emptyset\}$
 \end_inset
 
 .
@@ -2197,15 +2197,15 @@ Demostración:
 \end_inset
 
  y 
-\begin_inset Formula $G':=(V',E')$
+\begin_inset Formula $G'\coloneqq (V',E')$
 \end_inset
 
  dado por 
-\begin_inset Formula $V':=V^{L}\dot{\cup}\{x,y\}$
+\begin_inset Formula $V'\coloneqq V^{L}\dot{\cup}\{x,y\}$
 \end_inset
 
  y 
-\begin_inset Formula $E':=E^{L}\cup\{((i,u),x)\}_{(i,u)\in E}\cup\{((j,v),y)\}_{(j,v)\in E}$
+\begin_inset Formula $E'\coloneqq E^{L}\cup\{((i,u),x)\}_{(i,u)\in E}\cup\{((j,v),y)\}_{(j,v)\in E}$
 \end_inset
 
 .
@@ -2586,7 +2586,7 @@ Si
 
 .
  Si 
-\begin_inset Formula $e:=(u,v)\in E$
+\begin_inset Formula $e\coloneqq (u,v)\in E$
 \end_inset
 
 , como 
diff --git a/graf/n3.lyx b/graf/n3.lyx
index ed819e4..b2cfb39 100644
--- a/graf/n3.lyx
+++ b/graf/n3.lyx
@@ -155,11 +155,11 @@ teorema
 
 .
  Sean 
-\begin_inset Formula $u_{0}:=v_{0}:=u$
+\begin_inset Formula $u_{0}\coloneqq v_{0}\coloneqq u$
 \end_inset
 
 , 
-\begin_inset Formula $u_{p}:=u_{q}:=v$
+\begin_inset Formula $u_{p}\coloneqq u_{q}\coloneqq v$
 \end_inset
 
  e 
@@ -228,7 +228,7 @@ teorema
 \end_inset
 
 , sea 
-\begin_inset Formula $e:=(u,v)\in E$
+\begin_inset Formula $e\coloneqq (u,v)\in E$
 \end_inset
 
 , 
@@ -447,7 +447,7 @@ teorema
 \end_inset
 
  el ciclo que se forma al añadir 
-\begin_inset Formula $e:=(u,v)$
+\begin_inset Formula $e\coloneqq (u,v)$
 \end_inset
 
  a 
@@ -753,7 +753,7 @@ La altura de
 status open
 
 \begin_layout Plain Layout
-\begin_inset Formula $\lg x:=\log_{2}x$
+\begin_inset Formula $\lg x\coloneqq \log_{2}x$
 \end_inset
 
 .
@@ -792,15 +792,15 @@ Todos los niveles hasta el
 \end_inset
 
  se alcanza en 
-\begin_inset Formula $T':=(V',E')$
+\begin_inset Formula $T'\coloneqq (V',E')$
 \end_inset
 
  dado por 
-\begin_inset Formula $V':=\{b_{0},a_{1},b_{1},\dots,a_{h},b_{h}\}$
+\begin_inset Formula $V'\coloneqq \{b_{0},a_{1},b_{1},\dots,a_{h},b_{h}\}$
 \end_inset
 
  y 
-\begin_inset Formula $E':=\{(a_{k},b_{k-1}),(b_{k},b_{k-1})\}_{k\in\{1,\dots,h\}}$
+\begin_inset Formula $E'\coloneqq \{(a_{k},b_{k-1}),(b_{k},b_{k-1})\}_{k\in\{1,\dots,h\}}$
 \end_inset
 
 .
@@ -833,15 +833,15 @@ n\leq2^{h+1}-1\iff n+1\leq2^{h+1}\iff\lg(n+1)-1\leq h\overset{h\in\mathbb{Z}}{\i
 \end_inset
 
  La igualdad se alcanza en 
-\begin_inset Formula $T':=(V',E')$
+\begin_inset Formula $T'\coloneqq (V',E')$
 \end_inset
 
  con 
-\begin_inset Formula $V':=\{1,\dots,n\}$
+\begin_inset Formula $V'\coloneqq \{1,\dots,n\}$
 \end_inset
 
  y 
-\begin_inset Formula $E':=\{(k,\lfloor\frac{k}{2}\rfloor)\}_{k\in\{2,\dots,n\}}$
+\begin_inset Formula $E'\coloneqq \{(k,\lfloor\frac{k}{2}\rfloor)\}_{k\in\{2,\dots,n\}}$
 \end_inset
 
 .
@@ -1025,7 +1025,7 @@ mínimo
 \end_inset
 
  tales que 
-\begin_inset Formula $a:=(u,v)\in E$
+\begin_inset Formula $a\coloneqq (u,v)\in E$
 \end_inset
 
 , si 
@@ -1095,7 +1095,7 @@ mínimo
 \end_inset
 
  y 
-\begin_inset Formula $S:=(V,E_{0}\cup\{e\})$
+\begin_inset Formula $S\coloneqq (V,E_{0}\cup\{e\})$
 \end_inset
 
 , como 
@@ -1115,7 +1115,7 @@ mínimo
 \end_inset
 
  y 
-\begin_inset Formula $T_{1}:=(V,E_{1}:=E_{0}\cup\{e\}\setminus\{a\})$
+\begin_inset Formula $T_{1}\coloneqq (V,E_{1}\coloneqq E_{0}\cup\{e\}\setminus\{a\})$
 \end_inset
 
  tiene menor o igual (en concreto igual) peso que 
@@ -1371,7 +1371,9 @@ Mientras{$|V_1|<|V|$}{
 \backslash
 in V_1$ y $v_2
 \backslash
-in V_2$ con $e:=(v_1,v_2)
+in V_2$ con $e
+\backslash
+coloneqq (v_1,v_2)
 \backslash
 in E$ de peso mínimo
 \backslash
diff --git a/graf/n4.lyx b/graf/n4.lyx
index 5334582..3506c7c 100644
--- a/graf/n4.lyx
+++ b/graf/n4.lyx
@@ -90,7 +90,7 @@ Dada una red
 \end_inset
 
  y un camino 
-\begin_inset Formula $P:=v_{0}e_{1}v_{1}\cdots e_{k}v_{k}$
+\begin_inset Formula $P\coloneqq v_{0}e_{1}v_{1}\cdots e_{k}v_{k}$
 \end_inset
 
  en 
@@ -198,7 +198,7 @@ Como
 teorema
 \series default
 , sean 
-\begin_inset Formula $(V:=\{1,\dots,n\},E,\ell)$
+\begin_inset Formula $(V\coloneqq \{1,\dots,n\},E,\ell)$
 \end_inset
 
  una red conexa, 
@@ -311,7 +311,7 @@ status open
 \end_inset
 
 Sea 
-\begin_inset Formula $P:=si_{1}\cdots i_{k}$
+\begin_inset Formula $P\coloneqq si_{1}\cdots i_{k}$
 \end_inset
 
  un camino, y queremos ver que 
@@ -403,7 +403,7 @@ Si
 \begin_deeper
 \begin_layout Standard
 Sean 
-\begin_inset Formula $P:=st_{1}\cdots t_{p}j$
+\begin_inset Formula $P\coloneqq st_{1}\cdots t_{p}j$
 \end_inset
 
  un camino de 
@@ -423,11 +423,11 @@ Sean
 \end_inset
 
  y 
-\begin_inset Formula $t_{k:=i+1},\dots,t_{p},j\in R$
+\begin_inset Formula $t_{k\coloneqq i+1},\dots,t_{p},j\in R$
 \end_inset
 
 , entonces 
-\begin_inset Formula $P':=st_{1}\cdots t_{i}t_{k}$
+\begin_inset Formula $P'\coloneqq st_{1}\cdots t_{i}t_{k}$
 \end_inset
 
  cumple 
@@ -1761,7 +1761,7 @@ Si
 \end_inset
 
  tal que 
-\begin_inset Formula $G_{i}:=(V,E_{i}):=G+\{e_{1},\dots,e_{i}\}$
+\begin_inset Formula $G_{i}\coloneqq (V,E_{i})\coloneqq G+\{e_{1},\dots,e_{i}\}$
 \end_inset
 
  es hamiltoniano si y sólo si 
@@ -1769,7 +1769,7 @@ Si
 \end_inset
 
 , por lo que existe un camino hamiltoniano 
-\begin_inset Formula $(u=:u_{1})u_{2}\cdots(u_{n}:=v)$
+\begin_inset Formula $(u=:u_{1})u_{2}\cdots(u_{n}\coloneqq v)$
 \end_inset
 
  en 
@@ -1777,16 +1777,16 @@ Si
 \end_inset
 
 , con 
-\begin_inset Formula $n:=|V|$
+\begin_inset Formula $n\coloneqq |V|$
 \end_inset
 
 .
  Sean ahora 
-\begin_inset Formula $X:=\{i\in\{2,\dots,n-2\}\mid (u_{i},v)\in E_{k}\}$
+\begin_inset Formula $X\coloneqq \{i\in\{2,\dots,n-2\}\mid(u_{i},v)\in E_{k}\}$
 \end_inset
 
  e 
-\begin_inset Formula $Y:=\{i\in\{2,\dots,n-2\}\mid (u_{i+1},u)\in E_{k}\}$
+\begin_inset Formula $Y\coloneqq \{i\in\{2,\dots,n-2\}\mid(u_{i+1},u)\in E_{k}\}$
 \end_inset
 
 , se tiene 
diff --git a/graf/n5.lyx b/graf/n5.lyx
index 4ae5cf7..5914553 100644
--- a/graf/n5.lyx
+++ b/graf/n5.lyx
@@ -447,7 +447,7 @@ Sea
 \end_inset
 
  la partición, definimos 
-\begin_inset Formula $f(v):=0$
+\begin_inset Formula $f(v)\coloneqq 0$
 \end_inset
 
  para 
@@ -455,7 +455,7 @@ Sea
 \end_inset
 
  y 
-\begin_inset Formula $f(v):=1$
+\begin_inset Formula $f(v)\coloneqq 1$
 \end_inset
 
  para 
@@ -502,7 +502,7 @@ Se tiene
 \end_inset
 
  dada por 
-\begin_inset Formula $f(v):=[n(v)]_{2}$
+\begin_inset Formula $f(v)\coloneqq [n(v)]_{2}$
 \end_inset
 
  es una coloración de 
@@ -556,7 +556,7 @@ ciclo
 \begin_deeper
 \begin_layout Standard
 Como 
-\begin_inset Formula $C_{n}:=(V:=\{0,\dots,n-1\},\{\{i,[i+1]_{n}\}\}_{i\in V})$
+\begin_inset Formula $C_{n}\coloneqq (V\coloneqq \{0,\dots,n-1\},\{\{i,[i+1]_{n}\}\}_{i\in V})$
 \end_inset
 
  tiene ejes, 
@@ -614,7 +614,7 @@ Como
 \end_inset
 
 , y tomamos 
-\begin_inset Formula $f(i):=[i]_{2}$
+\begin_inset Formula $f(i)\coloneqq [i]_{2}$
 \end_inset
 
  para 
@@ -622,7 +622,7 @@ Como
 \end_inset
 
  y 
-\begin_inset Formula $f(0):=2$
+\begin_inset Formula $f(0)\coloneqq 2$
 \end_inset
 
 .
@@ -711,7 +711,7 @@ Si
 \begin_deeper
 \begin_layout Standard
 Sean 
-\begin_inset Formula $k:=\chi(G-v)$
+\begin_inset Formula $k\coloneqq \chi(G-v)$
 \end_inset
 
  y 
@@ -735,7 +735,7 @@ Sean
 \end_inset
 
  dada por 
-\begin_inset Formula $g(i):=f(i)$
+\begin_inset Formula $g(i)\coloneqq f(i)$
 \end_inset
 
  para 
@@ -743,7 +743,7 @@ Sean
 \end_inset
 
  y 
-\begin_inset Formula $g(v):=k+1$
+\begin_inset Formula $g(v)\coloneqq k+1$
 \end_inset
 
  es una 
@@ -1124,7 +1124,7 @@ Si todos los vértices de
 \end_inset
 
  con 
-\begin_inset Formula $\chi(H_{0}:=G_{0}-e_{1})=\chi(G_{0})$
+\begin_inset Formula $\chi(H_{0}\coloneqq G_{0}-e_{1})=\chi(G_{0})$
 \end_inset
 
 .
@@ -1172,7 +1172,7 @@ teorema
 Demostración:
 \series default
  Sea 
-\begin_inset Formula $k:=\chi(G)$
+\begin_inset Formula $k\coloneqq \chi(G)$
 \end_inset
 
  y supongamos 
@@ -1308,11 +1308,11 @@ Si
 \end_inset
 
  y 
-\begin_inset Formula $e:=(u,v)$
+\begin_inset Formula $e\coloneqq (u,v)$
 \end_inset
 
 , llamamos 
-\begin_inset Formula $G+e:=(V,E\cup\{e\})$
+\begin_inset Formula $G+e\coloneqq (V,E\cup\{e\})$
 \end_inset
 
 , y si 
@@ -1357,7 +1357,7 @@ Teorema de reducción:
 Demostración:
 \series default
  Sea 
-\begin_inset Formula $(u,v):=e$
+\begin_inset Formula $(u,v)\coloneqq e$
 \end_inset
 
 , las coloraciones 
@@ -1377,7 +1377,7 @@ Demostración:
 \end_inset
 
  haciendo 
-\begin_inset Formula $f(*):=f(u)=f(v)$
+\begin_inset Formula $f(*)\coloneqq f(u)=f(v)$
 \end_inset
 
 , y las coloraciones 
@@ -1576,7 +1576,7 @@ planar
 \end_inset
 
  tales que, para 
-\begin_inset Formula $e:=(u,v)\in E$
+\begin_inset Formula $e\coloneqq (u,v)\in E$
 \end_inset
 
 , 
@@ -1663,11 +1663,11 @@ estrella
 \end_inset
 
 , llamamos 
-\begin_inset Formula $f(v_{0}):=0$
+\begin_inset Formula $f(v_{0})\coloneqq 0$
 \end_inset
 
 , 
-\begin_inset Formula $f(v_{i}):=(\cos i/n,\sin i/n)$
+\begin_inset Formula $f(v_{i})\coloneqq (\cos i/n,\sin i/n)$
 \end_inset
 
  para 
@@ -1675,7 +1675,7 @@ estrella
 \end_inset
 
  y 
-\begin_inset Formula $g(v_{0},v_{i})(t):=tv_{i}$
+\begin_inset Formula $g(v_{0},v_{i})(t)\coloneqq tv_{i}$
 \end_inset
 
 .
@@ -1915,7 +1915,7 @@ Demostración:
 \end_inset
 
  y 
-\begin_inset Formula $c:=|F|$
+\begin_inset Formula $c\coloneqq |F|$
 \end_inset
 
 , como toda 
diff --git a/graf/n6.lyx b/graf/n6.lyx
index 6bf574a..c3d6148 100644
--- a/graf/n6.lyx
+++ b/graf/n6.lyx
@@ -158,7 +158,7 @@ Si
 \end_inset
 
 , llamamos 
-\begin_inset Formula $[x,y]:=(x_{1},\dots,x_{m},y_{1},\dots,y_{n})\in\mathbb{R}^{n+m}$
+\begin_inset Formula $[x,y]\coloneqq (x_{1},\dots,x_{m},y_{1},\dots,y_{n})\in\mathbb{R}^{n+m}$
 \end_inset
 
 ; si 
@@ -170,11 +170,11 @@ Si
 \end_inset
 
 , llamamos 
-\begin_inset Formula $[A,B]:=(c_{ij})\in{\cal M}_{n\times(p+q)}(\mathbb{R})$
+\begin_inset Formula $[A,B]\coloneqq (c_{ij})\in{\cal M}_{n\times(p+q)}(\mathbb{R})$
 \end_inset
 
  dada por 
-\begin_inset Formula $c_{ij}:=a_{ij}$
+\begin_inset Formula $c_{ij}\coloneqq a_{ij}$
 \end_inset
 
  para 
@@ -182,7 +182,7 @@ Si
 \end_inset
 
  y 
-\begin_inset Formula $c_{ij}:=b_{i(j-p)}$
+\begin_inset Formula $c_{ij}\coloneqq b_{i(j-p)}$
 \end_inset
 
  para 
@@ -190,7 +190,7 @@ Si
 \end_inset
 
 , y escribimos 
-\begin_inset Formula $[x_{1},\dots,x_{n}]:=[x_{1},[x_{2},\dots,x_{n}]]$
+\begin_inset Formula $[x_{1},\dots,x_{n}]\coloneqq [x_{1},[x_{2},\dots,x_{n}]]$
 \end_inset
 
  para 
@@ -198,7 +198,7 @@ Si
 \end_inset
 
  y 
-\begin_inset Formula $[x_{1}]:=x_{1}$
+\begin_inset Formula $[x_{1}]\coloneqq x_{1}$
 \end_inset
 
 .
@@ -222,11 +222,11 @@ teorema
 \end_inset
 
 , 
-\begin_inset Formula $P:=\{[x,y]\in\mathbb{R}^{p+q}\mid Ax+Gy\leq b\}$
+\begin_inset Formula $P\coloneqq \{[x,y]\in\mathbb{R}^{p+q}\mid Ax+Gy\leq b\}$
 \end_inset
 
  y 
-\begin_inset Formula $S:=\{[x,y]\in P\mid x\in\mathbb{Z}^{p}\}$
+\begin_inset Formula $S\coloneqq \{[x,y]\in P\mid x\in\mathbb{Z}^{p}\}$
 \end_inset
 
 , existen 
@@ -253,11 +253,11 @@ teorema
 Demostración:
 \series default
  Sean 
-\begin_inset Formula $S:=\{(x,y)\in\mathbb{Z}^{2}\mid y\leq\sqrt{2}x,x\geq0,y\geq0\}$
+\begin_inset Formula $S\coloneqq \{(x,y)\in\mathbb{Z}^{2}\mid y\leq\sqrt{2}x,x\geq0,y\geq0\}$
 \end_inset
 
  y 
-\begin_inset Formula $C:=\{(x,y)\mid y<\sqrt{2}x,x\geq0,y\geq0\}\cup\{0\}$
+\begin_inset Formula $C\coloneqq \{(x,y)\mid y<\sqrt{2}x,x\geq0,y\geq0\}\cup\{0\}$
 \end_inset
 
 .
@@ -283,7 +283,7 @@ Demostración:
 \end_inset
 
  y 
-\begin_inset Formula $p:=(1-t)a+tb$
+\begin_inset Formula $p\coloneqq (1-t)a+tb$
 \end_inset
 
 , si uno de 
@@ -406,11 +406,11 @@ Sean
 \end_inset
 
  y 
-\begin_inset Formula $P:=\{x\in\mathbb{R}^{n}\mid Ax\leq b\}$
+\begin_inset Formula $P\coloneqq \{x\in\mathbb{R}^{n}\mid Ax\leq b\}$
 \end_inset
 
 , si 
-\begin_inset Formula $P_{I}:=\text{ec}(P\cap\mathbb{Z}^{n})\neq\emptyset$
+\begin_inset Formula $P_{I}\coloneqq \text{ec}(P\cap\mathbb{Z}^{n})\neq\emptyset$
 \end_inset
 
 , para 
@@ -552,11 +552,11 @@ variable básica
 \end_inset
 
 , llamamos 
-\begin_inset Formula $x_{B}:=(x_{s_{1}},\dots,x_{s_{m}})$
+\begin_inset Formula $x_{B}\coloneqq (x_{s_{1}},\dots,x_{s_{m}})$
 \end_inset
 
 , 
-\begin_inset Formula $x_{N}:=(x_{t_{1}},\dots,x_{t_{n-m}})$
+\begin_inset Formula $x_{N}\coloneqq (x_{t_{1}},\dots,x_{t_{n-m}})$
 \end_inset
 
 , 
@@ -564,7 +564,7 @@ variable básica
 \end_inset
 
  y 
-\begin_inset Formula $\mathbf{n}(x_{1},\dots,x_{n-m}):=\sum_{k}e_{t_{k}}x_{k}$
+\begin_inset Formula $\mathbf{n}(x_{1},\dots,x_{n-m})\coloneqq \sum_{k}e_{t_{k}}x_{k}$
 \end_inset
 
 , 
@@ -609,7 +609,7 @@ factible
 
 \begin_layout Standard
 Dado 
-\begin_inset Formula $F:=\{Ax=b,x\geq0\}$
+\begin_inset Formula $F\coloneqq \{Ax=b,x\geq0\}$
 \end_inset
 
 , 
@@ -706,7 +706,7 @@ Lema de Veinott-Dantzig:
 \end_inset
 
 , 
-\begin_inset Formula $Q:=\{x\in\mathbb{R}^{n}\mid Ax=b,x\geq0\}$
+\begin_inset Formula $Q\coloneqq \{x\in\mathbb{R}^{n}\mid Ax=b,x\geq0\}$
 \end_inset
 
  es entero.
@@ -804,11 +804,11 @@ Sea
 \end_inset
 
  tal que 
-\begin_inset Formula $z:=y+(B^{-1})_{i}\geq0$
+\begin_inset Formula $z\coloneqq y+(B^{-1})_{i}\geq0$
 \end_inset
 
  y 
-\begin_inset Formula $b:=Bz=By+e_{i}$
+\begin_inset Formula $b\coloneqq Bz=By+e_{i}$
 \end_inset
 
 , 
@@ -828,11 +828,11 @@ Sea
 \end_inset
 
  todos los coeficientes enteros, luego 
-\begin_inset Formula $Q:=\{Ax=b,x\geq0\}$
+\begin_inset Formula $Q\coloneqq \{Ax=b,x\geq0\}$
 \end_inset
 
  es entero y 
-\begin_inset Formula $x:=\mathbf{b}z=\mathbf{b}B^{-1}b$
+\begin_inset Formula $x\coloneqq \mathbf{b}z=\mathbf{b}B^{-1}b$
 \end_inset
 
  es una solución básica factible de 
@@ -978,7 +978,7 @@ Dada una submatriz
 \end_inset
 
  es unimodular, con lo que 
-\begin_inset Formula $Q:=\{[x,y]\in\mathbb{R}^{n+m}\mid Ax+Iy=b,[x,y]\geq0\}$
+\begin_inset Formula $Q\coloneqq \{[x,y]\in\mathbb{R}^{n+m}\mid Ax+Iy=b,[x,y]\geq0\}$
 \end_inset
 
  es entero.
@@ -1003,7 +1003,7 @@ Dada una submatriz
 \end_inset
 
  es 
-\begin_inset Formula $P:=\{x\in\mathbb{R}^{n}\mid b=b,x\geq0,b-Ax\geq0\}=\{Ax\leq b,x\geq0\}$
+\begin_inset Formula $P\coloneqq \{x\in\mathbb{R}^{n}\mid b=b,x\geq0,b-Ax\geq0\}=\{Ax\leq b,x\geq0\}$
 \end_inset
 
 .
@@ -1016,7 +1016,7 @@ Dada una submatriz
 \end_inset
 
  es un punto extremo, pues si no lo fuera existirían 
-\begin_inset Formula $U:=[u,b-Au],V:=[v,b-Av]\in Q$
+\begin_inset Formula $U\coloneqq [u,b-Au],V\coloneqq [v,b-Av]\in Q$
 \end_inset
 
  distintos y 
@@ -1069,11 +1069,11 @@ Sean
 \end_inset
 
 , 
-\begin_inset Formula $P:=\{x\mid Ax\leq b,x\geq0\}$
+\begin_inset Formula $P\coloneqq \{x\mid Ax\leq b,x\geq0\}$
 \end_inset
 
 , 
-\begin_inset Formula $Q:=\{[x,y]\mid Ax+y=b,[x,y]\geq0\}$
+\begin_inset Formula $Q\coloneqq \{[x,y]\mid Ax+y=b,[x,y]\geq0\}$
 \end_inset
 
  y 
@@ -1293,7 +1293,7 @@ teorema
 \end_inset
 
  tal que, si 
-\begin_inset Formula $F_{2}:=F\setminus F_{1}$
+\begin_inset Formula $F_{2}\coloneqq F\setminus F_{1}$
 \end_inset
 
 , para 
@@ -1496,7 +1496,7 @@ Si las tareas se pueden hacer a la vez, lo que queremos minimizar es
 
 \begin_layout Standard
 Sean ahora 
-\begin_inset Formula $R:=(V:=\{1,\dots,n\},E,\omega)$
+\begin_inset Formula $R\coloneqq (V\coloneqq \{1,\dots,n\},E,\omega)$
 \end_inset
 
  una red y 
@@ -1595,7 +1595,7 @@ Para obtener el árbol generador minimal de
 \end_inset
 
 , llamamos 
-\begin_inset Formula $x_{ij}:=\chi_{E_{T}}(i,j)$
+\begin_inset Formula $x_{ij}\coloneqq \chi_{E_{T}}(i,j)$
 \end_inset
 
  para 
@@ -1643,7 +1643,7 @@ Otra posible formulación, con las mismas variables resulta de cambiar la
 
 \begin_layout Standard
 Para el problema del viajante de comercio sobre una red completa 
-\begin_inset Formula $R:=(V:=\{0,\dots,n-1\},E\mid =\{\{i,j\}\}_{i,j\in V,i\neq j},d)$
+\begin_inset Formula $R\coloneqq (V\coloneqq \{0,\dots,n-1\},E\coloneqq \{\{i,j\}\}_{i,j\in V,i\neq j},d)$
 \end_inset
 
 , existen varias formulaciones:
@@ -1774,7 +1774,7 @@ es
 
 .
  Llamando 
-\begin_inset Formula $n:=|V|$
+\begin_inset Formula $n\coloneqq |V|$
 \end_inset
 
 :
@@ -1783,7 +1783,7 @@ es
  & \min & {\textstyle \sum}_{ij}d_{ij}x_{ij}\\
  &  & {\textstyle \sum_{(i,j)\in E}}x_{ij} & =1 &  & \forall i\\
  &  & {\textstyle \sum_{(k,i)\in E}}x_{ki} & =1 &  & \forall i\\
- &  & u_{i}-u_{j}+nx_{ij} & \leq n-1 &  & \forall i,j\in\{1,\dots,n-1\}\mid (i,j)\in E\\
+ &  & u_{i}-u_{j}+nx_{ij} & \leq n-1 &  & \forall i,j\in\{1,\dots,n-1\}:(i,j)\in E\\
  &  & x_{ij} & \in\{0,1\} &  & \forall i,j\\
  &  & u_{i} & \in\mathbb{R}^{>0} &  & \forall i
 \end{alignat*}
@@ -1830,7 +1830,7 @@ Sea
 \end_inset
 
  la representación por variables de un ciclo hamiltoniano, llamamos 
-\begin_inset Formula $u_{i}:=t$
+\begin_inset Formula $u_{i}\coloneqq t$
 \end_inset
 
  si 
@@ -1928,7 +1928,7 @@ Dadas dos variables
 \end_inset
 
 , para definir una variable 
-\begin_inset Formula $y:=[x_{1}>x_{2}]$
+\begin_inset Formula $y\coloneqq [x_{1}>x_{2}]$
 \end_inset
 
  (
@@ -2053,7 +2053,7 @@ Si
 \end_inset
 
 , para definir 
-\begin_inset Formula $y:=\min\{x_{1},x_{2}\}$
+\begin_inset Formula $y\coloneqq \min\{x_{1},x_{2}\}$
 \end_inset
 
  añadimos 
@@ -2073,7 +2073,7 @@ Si
 \end_inset
 
 , y para definir 
-\begin_inset Formula $y:=\max\{x_{1},x_{2}\}$
+\begin_inset Formula $y\coloneqq \max\{x_{1},x_{2}\}$
 \end_inset
 
  añadimos 
diff --git a/graf/n7.lyx b/graf/n7.lyx
index dc0abb4..fbf8456 100644
--- a/graf/n7.lyx
+++ b/graf/n7.lyx
@@ -850,11 +850,11 @@ regla de Bland:
 \end_inset
 
 , 
-\begin_inset Formula $F:=\{x\mid Ax=b,x\geq0\}$
+\begin_inset Formula $F\coloneqq \{x\mid Ax=b,x\geq0\}$
 \end_inset
 
  y 
-\begin_inset Formula $P:=\{c\cdot x\}_{x\in F}$
+\begin_inset Formula $P\coloneqq \{c\cdot x\}_{x\in F}$
 \end_inset
 
 .
@@ -888,7 +888,7 @@ Si [...]
 \end_inset
 
  es la matriz formada por las columnas añadidas, escribimos 
-\begin_inset Formula $F^{*}:=\{[x,x^{*}]\in\mathbb{R}^{n+p}\mid Ax+Tx^{*}=b,[x,x^{*}]\geq0\}$
+\begin_inset Formula $F^{*}\coloneqq \{[x,x^{*}]\in\mathbb{R}^{n+p}\mid Ax+Tx^{*}=b,[x,x^{*}]\geq0\}$
 \end_inset
 
  y vemos que 
@@ -957,11 +957,11 @@ Método de penalización:
 \end_inset
 
  lo suficientemente grande, definimos 
-\begin_inset Formula $P_{M}:=\{c\cdot x+M\sum_{i}x_{i}^{*}\}_{[x,x^{*}]\in F^{*}}$
+\begin_inset Formula $P_{M}\coloneqq \{c\cdot x+M\sum_{i}x_{i}^{*}\}_{[x,x^{*}]\in F^{*}}$
 \end_inset
 
  si estamos minimizando o 
-\begin_inset Formula $P_{-M}:=\{c\cdot x-M\sum_{i}x_{i}^{*}\}_{[x,x^{*}]\in F^{*}}$
+\begin_inset Formula $P_{-M}\coloneqq \{c\cdot x-M\sum_{i}x_{i}^{*}\}_{[x,x^{*}]\in F^{*}}$
 \end_inset
 
  [si maximizamos].
@@ -1103,7 +1103,9 @@ to
 \backslash
 dots,m
 \backslash
-}$ tal que $B:=[A_{
+}$ tal que $B
+\backslash
+coloneqq [A_{
 \backslash
 sigma(1)},
 \backslash
@@ -1335,7 +1337,7 @@ Supongamos que tenemos una tabla de símplex óptima con parámetros
 
 , podemos añadir la restricción directamente a la tabla añadiendo lo siguiente,
  donde 
-\begin_inset Formula $t:=\beta-\sum_{j=1}^{n}\alpha_{j}x_{j}$
+\begin_inset Formula $t\coloneqq \beta-\sum_{j=1}^{n}\alpha_{j}x_{j}$
 \end_inset
 
  y 
@@ -1501,7 +1503,7 @@ desigualdad válida
  factibles.
  Se puede usar para mejorar las cotas en los nodos del árbol de ramificación.
  Llamamos 
-\begin_inset Formula $[[x]]:=x-\lfloor x\rfloor\in[0,1)$
+\begin_inset Formula $[[x]]\coloneqq x-\lfloor x\rfloor\in[0,1)$
 \end_inset
 
 .
@@ -1522,7 +1524,7 @@ Dados un problema entero puro
 \end_inset
 
  tal que 
-\begin_inset Formula $x_{k':=\sigma(k)}^{*}\notin\mathbb{Z}$
+\begin_inset Formula $x_{k'\coloneqq \sigma(k)}^{*}\notin\mathbb{Z}$
 \end_inset
 
 , entonces
@@ -1599,11 +1601,11 @@ Dados un problema entero puro
 \end_inset
 
  tal que 
-\begin_inset Formula $k':=\sigma(k)\in I$
+\begin_inset Formula $k'\coloneqq \sigma(k)\in I$
 \end_inset
 
  y 
-\begin_inset Formula $x_{k':=\sigma(k)}^{*}\notin\mathbb{Z}$
+\begin_inset Formula $x_{k'\coloneqq \sigma(k)}^{*}\notin\mathbb{Z}$
 \end_inset
 
 , entonces
@@ -1754,7 +1756,7 @@ Desigualdades de Chvátal-Gomory
 
 \begin_layout Standard
 Dado un problema entero puro con conjunto factible 
-\begin_inset Formula $P:=\{Ax\leq b,x\in\mathbb{N}^{n}\}$
+\begin_inset Formula $P\coloneqq \{Ax\leq b,x\in\mathbb{N}^{n}\}$
 \end_inset
 
 , donde