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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Maroon" title="c1">R</font><br/>  for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> being   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">V</font>,<font color="Maroon" title="c1">R</font> holds  <font color="Olive" title="b4">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">v1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">v2</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">v2</font></span>)</span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">v2</font> being   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c1">R</font> holds  <font color="Olive" title="b3">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">v1</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">v2</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">v2</font></span>)</span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v2</font> be   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c1">R</font> holds  <font color="Olive" title="b1">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">v2</font></span>)</span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c1">R</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">v2</font></span>)</span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>









<span class="lab"><font color="Green" title="E21">A1</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D6" target="_self" onmouseover="rs('rmod_4/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
2
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" onmouseover="rs('finseq_1/T44')" onmouseout="rh()">FINSEQ_1:44</a></span>
;<br/>
<a NAME="E2:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A2</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">1,2</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" onmouseover="rs('finseq_1/T2')" onmouseout="rh()">FINSEQ_1:2</a>, <a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E3:31"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">1,2</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E23">A3</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="rmod_4.html#D6" target="_self" onmouseover="rs('rmod_4/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c4">v2</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T17" onmouseover="rs('finseq_4/T17')" onmouseout="rh()">FINSEQ_4:17</a></span>
<br/>.= 
<font color="Maroon" title="c4">v2</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">v2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T17" onmouseover="rs('finseq_4/T17')" onmouseout="rh()">FINSEQ_4:17</a></span>
;<br/>
<a NAME="E5:31"/>
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">1,2</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="rmod_4.html#D6" target="_self" onmouseover="rs('rmod_4/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c3">v1</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T17" onmouseover="rs('finseq_4/T17')" onmouseout="rh()">FINSEQ_4:17</a></span>
<br/>.= 
<font color="Maroon" title="c3">v1</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_4.html#T17" onmouseover="rs('finseq_4/T17')" onmouseout="rh()">FINSEQ_4:17</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:31"/>
<font color="Maroon" title="c5">f</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">v2</font></span>)</span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="finseq_1.html#T44" onmouseover="rs('finseq_1/T44')" onmouseout="rh()">FINSEQ_1:44</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
