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<b>let </b><font color="Maroon">f</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">G</font> be   <a href="goboard1.html#NM1">Go-board</a>;<br/>



<b>assume </b><a NAME="E1:48"/><i><font color="Green">E59</font></i>: 
( <a href="pscomp_1.html#K13">proj1</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <a href="pscomp_1.html#K13">proj1</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="jordan1h.html#K2" target="_self">Values</a> <font color="Maroon">G</font></span>)</span> &amp; <a href="pscomp_1.html#K14">proj2</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <a href="pscomp_1.html#K14">proj2</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="jordan1h.html#K2" target="_self">Values</a> <font color="Maroon">G</font></span>)</span> )
 ;<br/>

<a NAME="E2:48"/>
 <a href="goboard1.html#K2">X_axis</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <a href="pscomp_1.html#K13">proj1</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:48"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="goboard1.html#K2">X_axis</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <a href="pscomp_1.html#K13">proj1</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T160">RELAT_1:160</a></i>;<br/>
<a NAME="E4:48"/><b>then </b><i><font color="Green">E60</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">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="triang_1.html#K2">SgmX</a> <a href="jordan1h.html#K1" target="_self">RealOrd</a> ,<span class="p1">(<span class="default"><a href="pscomp_1.html#K13">proj1</a>  <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:48"/>
 <a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <a href="pscomp_1.html#K14">proj2</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:48"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3">Y_axis</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <a href="pscomp_1.html#K14">proj2</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T160">RELAT_1:160</a></i>;<br/>
<a NAME="E7:48"/><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">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="triang_1.html#K2">SgmX</a> <a href="jordan1h.html#K1" target="_self">RealOrd</a> ,<span class="p1">(<span class="default"><a href="pscomp_1.html#K14">proj2</a>  <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><font color="Maroon">G</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">f</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">f</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="goboard2.html#K3">GoB</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="goboard2.html#D3">GOBOARD2:def 3</a></i>
;<br/><br/>


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