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<div class="add">

<b>let </b><font color="Maroon" title="c1">I</font> be  non <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a> <a href="group_1.html#V6" title="GROUP_1:attr.6">commutative</a> <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/>

<a NAME="E1:96"/><i><font color="Green" title="E75">A1</font></i>: 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="struct_0.html#D8" title="STRUCT_0:def.8">STRUCT_0:def 8</a></i>;<br/>
<a NAME="E2:96"/>
 <a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font> is <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1"><b>proof </b></a><div class="add">

<a NAME="E1:96_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">I</font> holds <br/> ( <span class="p1">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">I</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c4">t1</font> =  <a href="quofield.html#K23" title="QUOFIELD:func.23">quotient</a> <font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span>, <font color="Maroon" title="c5">t2</font> =  <a href="quofield.html#K23" title="QUOFIELD:func.23">quotient</a> <font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K1" title="QUOFIELD:func.1">Q.</a> <font color="Maroon" title="c1">I</font> ;<br/>
<a NAME="E2:96_1_1"/><i><font color="Green" title="E76">A2</font></i>: 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c4">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self" title="QUOFIELD:def.28">Def28</a></i>;<br/>
<a NAME="E3:96_1_1"/><i><font color="Green" title="E77">A3</font></i>: 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c5">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self" title="QUOFIELD:def.28">Def28</a></i>;<br/>
<a NAME="E4:96_1_1"/>
( <font color="Maroon" title="c4">t1</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">I</font> &amp; <font color="Maroon" title="c5">t2</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">I</font> )
 
<b>by </b><i><a class="ref" href="quofield.html#T2" target="_self" title="QUOFIELD:th.2">Th2</a></i>;<br/>
<a NAME="E5:96_1_1"/><b>then </b><i><font color="Green" title="E78">A4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#D5" title="VECTSP_2:def.5">VECTSP_2:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">sum</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</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" title="c4">t1</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K1" title="QUOFIELD:func.1">Q.</a> <font color="Maroon" title="c1">I</font> <b>by </b><i><a class="ref" href="quofield.html#D1" target="_self" title="QUOFIELD:def.1">Def1</a></i>;<br/>
<i><font color="Green" title="E79">A5</font></i>: <span class="p1">(<span class="default"><a href="quofield.html#K17" title="QUOFIELD:func.17">quotadd</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c4">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c5">t2</font></span>)</span> = 
 <a href="quofield.html#K10" title="QUOFIELD:func.10">qadd</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c4">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c5">t2</font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D12" target="_self" title="QUOFIELD:def.12">Def12</a></i>
<br/>.= 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K6" title="QUOFIELD:func.6">padd</a> <font color="Maroon" title="c4">t1</font>,<font color="Maroon" title="c5">t2</font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#T11" target="_self" title="QUOFIELD:th.11">Th11</a></i>
<br/>.= 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c6">sum</font>

;<br/>
<a NAME="E8:96_1_1"/><i><font color="Green" title="E80">A6</font></i>: 
<font color="Maroon" title="c5">t2</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_2"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a>  = 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:96"><i><font color="Green" title="E75">A1</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self" title="QUOFIELD:def.27">Def27</a></i>
<br/>.= 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E9:96_1_1"/><i><font color="Green" title="E81">A7</font></i>: 
<font color="Maroon" title="c4">t1</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_3"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a>  = 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:96"><i><font color="Green" title="E75">A1</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self" title="QUOFIELD:def.27">Def27</a></i>
<br/>.= 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E10:96_1_1"/><i><font color="Green" title="E82">A8</font></i>: 
<font color="Maroon" title="c5">t2</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_4"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a>  = 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:96"><i><font color="Green" title="E75">A1</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self" title="QUOFIELD:def.27">Def27</a></i>
<br/>.= 
<font color="Maroon" title="c3">y</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E11:96_1_1"/><i><font color="Green" title="E83">A9</font></i>: 
<font color="Maroon" title="c4">t1</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_5"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a>  = 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:96"><i><font color="Green" title="E75">A1</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self" title="QUOFIELD:def.27">Def27</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>
;<br/>


</div><b>end;</b></div>
<i><font color="Green" title="E84">A10</font></i>: <font color="Maroon" title="c6">sum</font> = 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="txt" href="quofield.html#E8:96_1_1"><i><font color="Green" title="E80">A6</font></i></a>, <a class="txt" href="quofield.html#E9:96_1_1"><i><font color="Green" title="E81">A7</font></i></a>, <a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">y</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="txt" href="quofield.html#E10:96_1_1"><i><font color="Green" title="E82">A8</font></i></a>, <a class="txt" href="quofield.html#E11:96_1_1"><i><font color="Green" title="E83">A9</font></i></a>, <a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">y</font></span>)</span> = 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" title="QUOFIELD:func.23">quotient</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">y</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self" title="QUOFIELD:def.28">Def28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">y</font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E1:96"><i><font color="Green" title="E75">A1</font></i></a>, <a class="txt" href="quofield.html#E2:96_1_1"><i><font color="Green" title="E76">A2</font></i></a>, <a class="txt" href="quofield.html#E3:96_1_1"><i><font color="Green" title="E77">A3</font></i></a>, <a class="txt" href="quofield.html#E7:96_1_1"><i><font color="Green" title="E79">A5</font></i></a>, <a class="txt" href="quofield.html#E12:96_1_1"><i><font color="Green" title="E84">A10</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self" title="QUOFIELD:def.27">Def27</a></i>
;<br/>

<b>reconsider </b><font color="Maroon" title="c7">prod</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">t2</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K1" title="QUOFIELD:func.1">Q.</a> <font color="Maroon" title="c1">I</font> <b>by </b><i><a class="txt" href="quofield.html#E5:96_1_1"><i><font color="Green" title="E78">A4</font></i></a>, <a class="ref" href="quofield.html#D1" target="_self" title="QUOFIELD:def.1">Def1</a></i>;<br/>
<i><font color="Green" title="E85">A11</font></i>: <span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c4">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c5">t2</font></span>)</span> = 
 <a href="quofield.html#K11" title="QUOFIELD:func.11">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c4">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c5">t2</font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D13" target="_self" title="QUOFIELD:def.13">Def13</a></i>
<br/>.= 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" title="QUOFIELD:func.7">pmult</a> <font color="Maroon" title="c4">t1</font>,<font color="Maroon" title="c5">t2</font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#T12" target="_self" title="QUOFIELD:th.12">Th12</a></i>
<br/>.= 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c7">prod</font>

;<br/>
<a NAME="E16:96_1_1"/><i><font color="Green" title="E86">A12</font></i>: 
<font color="Maroon" title="c7">prod</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">y</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="txt" href="quofield.html#E8:96_1_1"><i><font color="Green" title="E80">A6</font></i></a>, <a class="txt" href="quofield.html#E9:96_1_1"><i><font color="Green" title="E81">A7</font></i></a>, <a class="txt" href="quofield.html#E10:96_1_1"><i><font color="Green" title="E82">A8</font></i></a>, <a class="txt" href="quofield.html#E11:96_1_1"><i><font color="Green" title="E83">A9</font></i></a>, <a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">y</font></span>)</span> = 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" title="QUOFIELD:func.23">quotient</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">y</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self" title="QUOFIELD:def.28">Def28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">y</font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E1:96"><i><font color="Green" title="E75">A1</font></i></a>, <a class="txt" href="quofield.html#E2:96_1_1"><i><font color="Green" title="E76">A2</font></i></a>, <a class="txt" href="quofield.html#E3:96_1_1"><i><font color="Green" title="E77">A3</font></i></a>, <a class="txt" href="quofield.html#E15:96_1_1"><i><font color="Green" title="E85">A11</font></i></a>, <a class="txt" href="quofield.html#E16:96_1_1"><i><font color="Green" title="E86">A12</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self" title="QUOFIELD:def.27">Def27</a></i>
;<br/>

<b>reconsider </b><font color="Maroon" title="c8">res3</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K1" title="QUOFIELD:func.1">Q.</a> <font color="Maroon" title="c1">I</font> <b>by </b><i><a class="txt" href="quofield.html#E1:96"><i><font color="Green" title="E75">A1</font></i></a>, <a class="ref" href="quofield.html#D1" target="_self" title="QUOFIELD:def.1">Def1</a></i>;<br/>
<a NAME="E19:96_1_1"/><i><font color="Green" title="E87">A13</font></i>: 
 <a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c8">res3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_10"><b>proof </b></a><div class="add">

<a NAME="E1:96_1_1_10"/><i><font color="Green" title="E88">A14</font></i>: 
for <font color="Olive" title="b1">u</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font> holds <br/><font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c8">res3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_10_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:96_1_1_10_1"/><i><font color="Green" title="E89">A15</font></i>: 
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c10">u</font> = <font color="Maroon" title="c9">u</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K1" title="QUOFIELD:func.1">Q.</a> <font color="Maroon" title="c1">I</font> ;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">res3</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c10">u</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> 
<b>by </b><i><a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></i>
<br/>.= 
<font color="Maroon" title="c10">u</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> 
<b>by </b><i><a class="txt" href="quofield.html#E1:96_1_1_10_1"><i><font color="Green" title="E89">A15</font></i></a>, <a class="ref" href="quofield.html#D9" target="_self" title="QUOFIELD:def.9">Def9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">res3</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E4:96_1_1_10_1"/>
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c8">res3</font>
 <b>by </b><i><a class="ref" href="quofield.html#D4" target="_self" title="QUOFIELD:def.4">Def4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:96_1_1_10"/>
for <font color="Olive" title="b1">u</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c8">res3</font> holds <br/><font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_1_10_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:96_1_1_10_2"/><i><font color="Green" title="E89">A16</font></i>: 
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c8">res3</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c10">u</font> = <font color="Maroon" title="c9">u</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K1" title="QUOFIELD:func.1">Q.</a> <font color="Maroon" title="c1">I</font> ;<br/>
<font color="Maroon" title="c10">u</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">res3</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">res3</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a> </span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E1:96_1_1_10_2"><i><font color="Green" title="E89">A16</font></i></a>, <a class="ref" href="quofield.html#D4" target="_self" title="QUOFIELD:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c10">u</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> 
<b>by </b><i><a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></i>
;<br/>
<b>hence </b><a NAME="E4:96_1_1_10_2"/>
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font>
 <b>by </b><i><a class="ref" href="quofield.html#D9" target="_self" title="QUOFIELD:def.9">Def9</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:96_1_1_10"/>
 <a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <font color="Maroon" title="c8">res3</font>
 <b>by </b><i><a class="txt" href="quofield.html#E1:96_1_1_10"><i><font color="Green" title="E88">A14</font></i></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


</div><b>end;</b></div>
<b>thus </b><span class="p1">(<span class="default"><a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="quofield.html#K12" title="QUOFIELD:func.12">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" title="QUOFIELD:func.23">quotient</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D28" target="_self" title="QUOFIELD:def.28">Def28</a></i>
<br/>.= 
 <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E1:96"><i><font color="Green" title="E75">A1</font></i></a>, <a class="txt" href="quofield.html#E19:96_1_1"><i><font color="Green" title="E87">A13</font></i></a>, <a class="ref" href="quofield.html#D27" target="_self" title="QUOFIELD:def.27">Def27</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E2:96_1"/><b>then </b>
(  <a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font> is <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> &amp;  <a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font> is <a href="group_6.html#V1" title="GROUP_6:attr.1">multiplicative</a> &amp;  <a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font> is <a href="group_1.html#V7" title="GROUP_1:attr.7">unity-preserving</a> )
 
<b>by </b><i><a class="ref" href="group_1.html#D17" title="GROUP_1:def.17">GROUP_1:def 17</a>, <a class="ref" href="group_6.html#D7" title="GROUP_6:def.7">GROUP_6:def 7</a>, <a class="ref" href="grcat_1.html#D13" title="GRCAT_1:def.13">GRCAT_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E3:96_1"/>
 <a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font> is <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>
 <b>by </b><i><a class="ref" href="quofield.html#D21" target="_self" title="QUOFIELD:def.21">Def21</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:96"/>
 <a href="quofield.html#K24" title="QUOFIELD:func.24">canHom</a> <font color="Maroon" title="c1">I</font> is <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>
 ;<br/>


</div>
