<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<b>assume </b><a NAME="E1:11"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green">E14</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="goboard9.html#T10" target="_self">Th10</a></i>;<br/>
<i><font color="Green">E15</font></i>:  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2">Incr</a> <span class="p2">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="goboard2.html#D2">GOBOARD2:def 2</a></i>
<br/>.= 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E2:11"><i><font color="Green">E14</font></i></a>, <a class="ref" href="finseq_5.html#T60">FINSEQ_5:60</a></i>
;<br/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2">Incr</a> <span class="p2">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="goboard2.html#D2">GOBOARD2:def 2</a></i>
<br/>.= 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E2:11"><i><font color="Green">E14</font></i></a>, <a class="ref" href="finseq_5.html#T60">FINSEQ_5:60</a></i>
;<br/>
<a NAME="E5:11"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="goboard2.html#K2">Incr</a> <span class="p1">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard2.html#K2">Incr</a> <span class="p1">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard9.html#E3:11"><i><font color="Green">E15</font></i></a>, <a class="ref" href="goboard2.html#D2">GOBOARD2:def 2</a></i>;<br/>
<a NAME="E6:11"/><i><font color="Green">E17</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="goboard9.html#E1:11"><i><font color="Green">E13</font></i></a>, <a class="ref" href="goboard9.html#T11" target="_self">Th11</a></i>;<br/>
<i><font color="Green">E18</font></i>:  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2">Incr</a> <span class="p2">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="goboard2.html#D2">GOBOARD2:def 2</a></i>
<br/>.= 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E6:11"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_5.html#T60">FINSEQ_5:60</a></i>
;<br/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2">Incr</a> <span class="p2">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="goboard2.html#D2">GOBOARD2:def 2</a></i>
<br/>.= 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E6:11"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_5.html#T60">FINSEQ_5:60</a></i>
;<br/>
<a NAME="E9:11"/><b>then </b>
 <a href="goboard2.html#K2">Incr</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard2.html#K2">Incr</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard9.html#E7:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="goboard2.html#D2">GOBOARD2:def 2</a></i>;<br/>
<b>hence </b> <a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font> = 
 <a href="goboard2.html#K1">GoB</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2">Incr</a> <span class="p2">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="goboard2.html#K2">Incr</a> <span class="p2">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E5:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="goboard2.html#D3">GOBOARD2:def 3</a></i>
<br/>.= 
 <a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="goboard2.html#D3">GOBOARD2:def 3</a></i>
;<br/><br/>


</div>
