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<b>let </b><font color="Maroon" title="c1">G2</font>, <font color="Maroon" title="c2">G3</font>, <font color="Maroon" title="c3">G1</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c4">G</font> be    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">G3</font>;<br/><b>let </b><font color="Maroon" title="c5">F</font> be    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c1">G2</font>;<br/>









<b>assume </b><a NAME="E1:29"/><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c3">G1</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Maroon" title="c1">G2</font> &amp; <font color="Maroon" title="c1">G2</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Maroon" title="c2">G3</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">G3</font><b> such that </b><br/><a NAME="E3:29"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(# <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">G3</font>,<font color="Maroon" title="c6">g</font> #)
 <b>by </b><i><a class="txt" href="ringcat1.html#E23"><i><font color="Green" title="E15">Lm8</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c1">G2</font><b> such that </b><br/><a NAME="E5:29"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(# <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c7">f</font> #)
 <b>by </b><i><a class="txt" href="ringcat1.html#E1:29"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="ringcat1.html#E23"><i><font color="Green" title="E15">Lm8</font></i></a></i>;<br/>
 <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <font color="Maroon" title="c4">G</font> = 
<font color="Maroon" title="c1">G2</font>
<b>by </b><i><a class="txt" href="ringcat1.html#E1:29"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="ringcat1.html#D9" target="_self" title="RINGCAT1:def.9">Def9</a></i>
<br/>.= 
 <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="txt" href="ringcat1.html#E1:29"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="ringcat1.html#D9" target="_self" title="RINGCAT1:def.9">Def9</a></i>
;<br/>
<a NAME="E7:29"/><b>then </b>
<font color="Maroon" title="c4">G</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(# <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c2">G3</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">f</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="ringcat1.html#E3:29"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="ringcat1.html#E5:29"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="ringcat1.html#D10" target="_self" title="RINGCAT1:def.10">Def10</a></i>;<br/>
<a NAME="E8:29"/><b>then </b><i><font color="Green" title="E22">A4</font></i>: 
(  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">G1</font> &amp;  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G3</font> )
 
;<br/>
<a NAME="E9:29"/>
<font color="Maroon" title="c3">G1</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Maroon" title="c2">G3</font>
 
<b>by </b><i><a class="txt" href="ringcat1.html#E1:29"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="ringcat1.html#T8" target="_self" title="RINGCAT1:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E10:29"/>
<font color="Maroon" title="c4">G</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Maroon" title="c5">F</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c2">G3</font>
 <b>by </b><i><a class="txt" href="ringcat1.html#E8:29"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="ringcat1.html#D9" target="_self" title="RINGCAT1:def.9">Def9</a></i>;<br/>


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