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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="lattice5.html#M2" target="_self">ExtensionSeq</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="lattice5.html#K17" target="_self">BasicDF</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="lattice5.html#NM4">distance_function</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:81"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span>  )
 <b>and </b><br/><a NAME="E2:81"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E3:81"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> 0</span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:81"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="lattice5.html#E1:81"><i><font color="Green">E63</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E8:81"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> 
 <b>by </b><i><a class="txt" href="lattice5.html#E6:81"><i><font color="Green">E65</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">c<sub>13</sub></font> being   <a href="lattice5.html#NM4">distance_function</a> of <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>14</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">c<sub>15</sub></font> being   <a href="lattice5.html#NM4">distance_function</a> of <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E10:81"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="lattice5.html#R2" target="_self">is_extension_of</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>and </b><br/><a NAME="E11:81"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="lattice5.html#D21" target="_self">Def21</a></i>;<br/>
<a NAME="E12:81"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E11:81"><i><font color="Green">E68</font></i></a>, <a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<a NAME="E13:81"/><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E11:81"><i><font color="Green">E68</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/>
<a NAME="E14:81"/><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E11:81"><i><font color="Green">E68</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/>
<a NAME="E15:81"/><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E11:81"><i><font color="Green">E68</font></i></a>, <a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<a NAME="E16:81"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span> 
 
<b>by </b><i><a class="txt" href="lattice5.html#E12:81"><i><font color="Green">E69</font></i></a></i>;<br/>
<a NAME="E17:81"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:81"><i><font color="Green">E63</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E18:81"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span> 
 
<b>by </b><i><a class="txt" href="lattice5.html#E15:81"><i><font color="Green">E72</font></i></a></i>;<br/>
<a NAME="E19:81"/><b>then </b><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:81"><i><font color="Green">E63</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E20:81"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span> 
 
<b>by </b><i><a class="txt" href="lattice5.html#E14:81"><i><font color="Green">E71</font></i></a></i>;<br/>
<a NAME="E21:81"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:81"><i><font color="Green">E63</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E22:81"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E6:81"><i><font color="Green">E65</font></i></a>, <a class="txt" href="lattice5.html#E8:81"><i><font color="Green">E66</font></i></a>, <a class="txt" href="lattice5.html#E11:81"><i><font color="Green">E68</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>16</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E24:81"/><i><font color="Green">E77</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="lattice5.html#E1:81"><i><font color="Green">E63</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E26:81"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> 
 <b>by </b><i><a class="txt" href="lattice5.html#E24:81"><i><font color="Green">E77</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>18</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">c<sub>19</sub></font> being   <a href="lattice5.html#NM4">distance_function</a> of <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>20</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">c<sub>21</sub></font> being   <a href="lattice5.html#NM4">distance_function</a> of <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E28:81"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font> <a href="lattice5.html#R2" target="_self">is_extension_of</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 <b>and </b><br/><a NAME="E29:81"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="lattice5.html#D21" target="_self">Def21</a></i>;<br/>
<a NAME="E30:81"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E29:81"><i><font color="Green">E80</font></i></a>, <a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<a NAME="E31:81"/><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E29:81"><i><font color="Green">E80</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/>
<a NAME="E32:81"/><i><font color="Green">E83</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E29:81"><i><font color="Green">E80</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/>
<a NAME="E33:81"/><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E29:81"><i><font color="Green">E80</font></i></a>, <a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<a NAME="E34:81"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span> 
 
<b>by </b><i><a class="txt" href="lattice5.html#E30:81"><i><font color="Green">E81</font></i></a></i>;<br/>
<a NAME="E35:81"/><b>then </b><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:81"><i><font color="Green">E63</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E36:81"/>
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span> 
 
<b>by </b><i><a class="txt" href="lattice5.html#E33:81"><i><font color="Green">E84</font></i></a></i>;<br/>
<a NAME="E37:81"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:81"><i><font color="Green">E63</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E38:81"/>
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : verum </span>}</span> 
 
<b>by </b><i><a class="txt" href="lattice5.html#E32:81"><i><font color="Green">E83</font></i></a></i>;<br/>
<a NAME="E39:81"/><b>then </b><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:81"><i><font color="Green">E63</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E40:81"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E24:81"><i><font color="Green">E77</font></i></a>, <a class="txt" href="lattice5.html#E26:81"><i><font color="Green">E78</font></i></a>, <a class="txt" href="lattice5.html#E29:81"><i><font color="Green">E80</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="81_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:81_1"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="81_1_1"><b>suppose </b></a><a NAME="E1:81_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/><div class="add"><a NAME="E2:81_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="lattice5.html#E13:81"><i><font color="Green">E70</font></i></a>, <a class="txt" href="lattice5.html#E31:81"><i><font color="Green">E82</font></i></a>, <a class="ref" href="lattice5.html#T41" target="_self">Th41</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>18</sub></font> <b>by </b><i><a class="txt" href="lattice5.html#E22:81"><i><font color="Green">E76</font></i></a>, <a class="txt" href="lattice5.html#E24:81"><i><font color="Green">E77</font></i></a>, <a class="txt" href="lattice5.html#E26:81"><i><font color="Green">E78</font></i></a>, <a class="txt" href="lattice5.html#E29:81"><i><font color="Green">E80</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/><a NAME="E4:81_1_1"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>18</sub></font> )
 ;<br/><a NAME="E5:81_1_1"/><i><font color="Green">E90</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>19</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E35:81"><i><font color="Green">E85</font></i></a>, <a class="txt" href="lattice5.html#E5:81_1_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>19</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font>

;<br/><b>then consider </b><font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>26</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>20</sub></font><b> such that </b><br/><a NAME="E8:81_1_1"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E9:81_1_1"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E10:81_1_1"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E11:81_1_1"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="lattice5.html#E2:81"><i><font color="Green">E64</font></i></a>, <a class="txt" href="lattice5.html#E28:81"><i><font color="Green">E79</font></i></a>, <a class="ref" href="lattice5.html#T40" target="_self">Th40</a></i>;<br/><a NAME="E12:81_1_1"/>
( <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font> )
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>29</sub></font> = <font color="Maroon">c<sub>26</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="lattice5.html#E39:81"><i><font color="Green">E87</font></i></a></i>;<br/><a NAME="E14:81_1_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E15:81_1_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="lattice5.html#E31:81"><i><font color="Green">E82</font></i></a>, <a class="txt" href="lattice5.html#E32:81"><i><font color="Green">E83</font></i></a>, <a class="ref" href="lattice5.html#T41" target="_self">Th41</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>30</sub></font> = <font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>31</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>20</sub></font> <b>by </b><i><a class="txt" href="lattice5.html#E4:81_1_1"><i><font color="Green">E89</font></i></a></i>;<br/><a NAME="E17:81_1_1"/><i><font color="Green">E95</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>27</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>28</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>29</sub></font>
;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>27</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>21</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E37:81"><i><font color="Green">E86</font></i></a>, <a class="txt" href="lattice5.html#E17:81_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E8:81_1_1"><i><font color="Green">E91</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>29</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>21</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E37:81"><i><font color="Green">E86</font></i></a>, <a class="txt" href="lattice5.html#E17:81_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E9:81_1_1"><i><font color="Green">E92</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>21</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E37:81"><i><font color="Green">E86</font></i></a>, <a class="txt" href="lattice5.html#E17:81_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E10:81_1_1"><i><font color="Green">E93</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>31</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>21</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>31</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E37:81"><i><font color="Green">E86</font></i></a>, <a class="txt" href="lattice5.html#E17:81_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E11:81_1_1"><i><font color="Green">E94</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="81_1_2"><b>suppose </b></a><a NAME="E1:81_1_2"/>
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><div class="add"><a NAME="E2:81_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="lattice5.html#E13:81"><i><font color="Green">E70</font></i></a>, <a class="txt" href="lattice5.html#E31:81"><i><font color="Green">E82</font></i></a>, <a class="ref" href="lattice5.html#T41" target="_self">Th41</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>12</sub></font> <b>by </b><i><a class="txt" href="lattice5.html#E6:81"><i><font color="Green">E65</font></i></a>, <a class="txt" href="lattice5.html#E8:81"><i><font color="Green">E66</font></i></a>, <a class="txt" href="lattice5.html#E11:81"><i><font color="Green">E68</font></i></a>, <a class="txt" href="lattice5.html#E40:81"><i><font color="Green">E88</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/><a NAME="E4:81_1_2"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> )
 ;<br/><a NAME="E5:81_1_2"/><i><font color="Green">E90</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E17:81"><i><font color="Green">E73</font></i></a>, <a class="txt" href="lattice5.html#E5:81_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>13</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font>

;<br/><b>then consider </b><font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>26</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>14</sub></font><b> such that </b><br/><a NAME="E8:81_1_2"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E9:81_1_2"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E10:81_1_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E11:81_1_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="lattice5.html#E2:81"><i><font color="Green">E64</font></i></a>, <a class="txt" href="lattice5.html#E10:81"><i><font color="Green">E67</font></i></a>, <a class="ref" href="lattice5.html#T40" target="_self">Th40</a></i>;<br/><a NAME="E12:81_1_2"/>
( <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> )
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>29</sub></font> = <font color="Maroon">c<sub>26</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="lattice5.html#E21:81"><i><font color="Green">E75</font></i></a></i>;<br/><a NAME="E14:81_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E15:81_1_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="lattice5.html#E13:81"><i><font color="Green">E70</font></i></a>, <a class="txt" href="lattice5.html#E14:81"><i><font color="Green">E71</font></i></a>, <a class="ref" href="lattice5.html#T41" target="_self">Th41</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>30</sub></font> = <font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>31</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>14</sub></font> <b>by </b><i><a class="txt" href="lattice5.html#E4:81_1_2"><i><font color="Green">E89</font></i></a></i>;<br/><a NAME="E17:81_1_2"/><i><font color="Green">E95</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>27</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>28</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>29</sub></font>
;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>27</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>24</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E19:81"><i><font color="Green">E74</font></i></a>, <a class="txt" href="lattice5.html#E17:81_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E8:81_1_2"><i><font color="Green">E91</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>29</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E19:81"><i><font color="Green">E74</font></i></a>, <a class="txt" href="lattice5.html#E17:81_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E9:81_1_2"><i><font color="Green">E92</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E19:81"><i><font color="Green">E74</font></i></a>, <a class="txt" href="lattice5.html#E17:81_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E10:81_1_2"><i><font color="Green">E93</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>31</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>31</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice5.html#E19:81"><i><font color="Green">E74</font></i></a>, <a class="txt" href="lattice5.html#E17:81_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E11:81_1_2"><i><font color="Green">E94</font></i></a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
