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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="group_1.html#V7">commutative</a> non <a href="vectsp_1.html#V10">degenerated</a> <a href="vectsp_2.html#V2">domRing-like</a> <a href="funcsdom.html#NM1">Ring</a>;<br/>

<a NAME="E1:97"/><i><font color="Green">E79</font></i>: 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/>
<a NAME="E2:97"/>
 <a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="quofield.html#V1" target="_self">RingHomomorphism</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><b>proof </b></a><div class="add">

<a NAME="E1:97_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K10">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="quofield.html#K23" target="_self">quotient</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>, <font color="Maroon">c<sub>5</sub></font> =  <a href="quofield.html#K23" target="_self">quotient</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E2:97_1_1"/><i><font color="Green">E80</font></i>: 
 <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self">Def28</a></i>;<br/>
<a NAME="E3:97_1_1"/><i><font color="Green">E81</font></i>: 
 <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self">Def28</a></i>;<br/>
<a NAME="E4:97_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="quofield.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E5:97_1_1"/><b>then </b><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1">]</a></span> as    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="quofield.html#D1" target="_self">Def1</a></i>;<br/>
<i><font color="Green">E83</font></i>: <span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="quofield.html#K10" target="_self">qadd</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D12" target="_self">Def12</a></i>
<br/>.= 
 <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K6" target="_self">padd</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#T11" target="_self">Th11</a></i>
<br/>.= 
 <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>6</sub></font>

;<br/>
<a NAME="E8:97_1_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_2"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  = 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K3">`2</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:97"><i><font color="Green">E79</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self">Def27</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E9:97_1_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_3"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  = 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K3">`2</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:97"><i><font color="Green">E79</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self">Def27</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E10:97_1_1"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_4"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  = 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K2">`1</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:97"><i><font color="Green">E79</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self">Def27</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E11:97_1_1"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_5"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  = 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K2">`1</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:97"><i><font color="Green">E79</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self">Def27</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>
;<br/>


</div><b>end;</b></div>
<i><font color="Green">E88</font></i>: <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="quofield.html#E8:97_1_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="quofield.html#E9:97_1_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="quofield.html#E10:97_1_1"><i><font color="Green">E86</font></i></a>, <a class="txt" href="quofield.html#E11:97_1_1"><i><font color="Green">E87</font></i></a>, <a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
;<br/>
<i><font color="Green">E89</font></i>: <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" target="_self">quotient</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self">Def28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E1:97"><i><font color="Green">E79</font></i></a>, <a class="txt" href="quofield.html#E7:97_1_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="quofield.html#E12:97_1_1"><i><font color="Green">E88</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self">Def27</a></i>
<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E2:97_1_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="quofield.html#E3:97_1_1"><i><font color="Green">E81</font></i></a></i>
<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1">]</a></span> as    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="quofield.html#E5:97_1_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="quofield.html#D1" target="_self">Def1</a></i>;<br/>
<i><font color="Green">E90</font></i>: <span class="p1">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D13" target="_self">Def13</a></i>
<br/>.= 
 <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#T12" target="_self">Th12</a></i>
<br/>.= 
 <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>7</sub></font>

;<br/>
<a NAME="E16:97_1_1"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="txt" href="quofield.html#E8:97_1_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="quofield.html#E9:97_1_1"><i><font color="Green">E85</font></i></a>, <a class="txt" href="quofield.html#E10:97_1_1"><i><font color="Green">E86</font></i></a>, <a class="txt" href="quofield.html#E11:97_1_1"><i><font color="Green">E87</font></i></a>, <a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>;<br/>
<i><font color="Green">E92</font></i>: <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" target="_self">quotient</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self">Def28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E1:97"><i><font color="Green">E79</font></i></a>, <a class="txt" href="quofield.html#E15:97_1_1"><i><font color="Green">E90</font></i></a>, <a class="txt" href="quofield.html#E16:97_1_1"><i><font color="Green">E91</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self">Def27</a></i>
<br/>.= 
the <a href="group_1.html#U1">mult</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E2:97_1_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="quofield.html#E3:97_1_1"><i><font color="Green">E81</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span> as    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="quofield.html#E1:97"><i><font color="Green">E79</font></i></a>, <a class="ref" href="quofield.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E19:97_1_1"/><i><font color="Green">E93</font></i>: 
 <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>8</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_10"><b>proof </b></a><div class="add">

<a NAME="E1:97_1_1_10"/><i><font color="Green">E94</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>8</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_10_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:97_1_1_10_1"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K2" target="_self">`1</a> 
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K3" target="_self">`2</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:97_1_1_10_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="quofield.html#D9" target="_self">Def9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E4:97_1_1_10_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="quofield.html#D4" target="_self">Def4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:97_1_1_10"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_10_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:97_1_1_10_2"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E1:97_1_1_10_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="quofield.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="quofield.html#K3" target="_self">`2</a> 
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
;<br/>
<b>hence </b><a NAME="E4:97_1_1_10_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="quofield.html#D9" target="_self">Def9</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:97_1_1_10"/>
 <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E1:97_1_1_10"><i><font color="Green">E94</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div><b>end;</b></div>
<span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
 <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" target="_self">quotient</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self">Def28</a></i>
<br/>.= 
 <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="quofield.html#E1:97"><i><font color="Green">E79</font></i></a>, <a class="txt" href="quofield.html#E19:97_1_1"><i><font color="Green">E93</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self">Def27</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E65"><i><font color="Green">Lemma55</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E21:97_1_1"/>
( <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="quofield.html#E13:97_1_1"><i><font color="Green">E89</font></i></a>, <a class="txt" href="quofield.html#E17:97_1_1"><i><font color="Green">E92</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:97_1"/><b>then </b>
(  <a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="grcat_1.html#V1">additive</a> &amp;  <a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="group_6.html#V1">multiplicative</a> &amp;  <a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="endalg.html#V1">unity-preserving</a> )
 
<b>by </b><i><a class="ref" href="endalg.html#D8">ENDALG:def 8</a>, <a class="ref" href="group_6.html#D7">GROUP_6:def 7</a>, <a class="ref" href="grcat_1.html#D13">GRCAT_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E3:97_1"/>
 <a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="quofield.html#V1" target="_self">RingHomomorphism</a>
 <b>by </b><i><a class="ref" href="quofield.html#D21" target="_self">Def21</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:97"/>
 <a href="quofield.html#K24" target="_self">canHom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="quofield.html#V1" target="_self">RingHomomorphism</a>
 ;<br/>


</div>
