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<b>let </b><font color="Maroon">R</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_2.html#NM7">RightMod</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v2</font> be   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">V</font>,<font color="Maroon">R</font>;<br/>









<i><font color="Green">E48</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rmod_4.html#K4" target="_self">(#)</a> <span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i/>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/>
<a NAME="E2:32"/><b>then </b><i><font color="Green">E49</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rmod_4.html#K4" target="_self">(#)</a> <span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> &amp; 1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> &amp; 2 <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>then </b><i><font color="Green">E50</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rmod_4.html#K4" target="_self">(#)</a> <span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span> <a href="vectsp_2.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">v1</font> <a href="vectsp_2.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>
<br/>.= 
<font color="Maroon">v1</font> <a href="vectsp_2.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v1</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rmod_4.html#K4" target="_self">(#)</a> <span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> 2 = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span> <a href="vectsp_2.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">v2</font> <a href="vectsp_2.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>
<br/>.= 
<font color="Maroon">v2</font> <a href="vectsp_2.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v2</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>
;<br/>
<b>hence </b><a NAME="E5:32"/>
<font color="Maroon">f</font> <a href="rmod_4.html#K4" target="_self">(#)</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">v1</font> <a href="vectsp_2.html#K6">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">v2</font> <a href="vectsp_2.html#K6">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v2</font></span>)</span></span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>


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