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<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="ringcat1.html#NM1">RingMorphism</a><b> such that </b><br/><a NAME="E2:14_1_1"/><i><font color="Green">E8</font></i>: 
(  <a href="ringcat1.html#K1" target="_self">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="ringcat1.html#K2" target="_self">cod</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="ringcat1.html#E1:14"><i><font color="Green">E7</font></i></a>, <a class="ref" href="ringcat1.html#D8" target="_self">Def8</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# the <a href="ringcat1.html#U1" target="_self">Dom</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="ringcat1.html#U2" target="_self">Cod</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="ringcat1.html#U3" target="_self">Fun</a> of <font color="Maroon">c<sub>3</sub></font> #);<br/>
<a NAME="E3:14_1_1"/>
(  <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# the <a href="ringcat1.html#U1" target="_self">Dom</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="ringcat1.html#U2" target="_self">Cod</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="ringcat1.html#U3" target="_self">Fun</a> of <font color="Maroon">c<sub>3</sub></font> #) is   <a href="ringcat1.html#NM1">RingMorphism</a> &amp;  <a href="ringcat1.html#K1" target="_self">dom</a> <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# the <a href="ringcat1.html#U1" target="_self">Dom</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="ringcat1.html#U2" target="_self">Cod</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="ringcat1.html#U3" target="_self">Fun</a> of <font color="Maroon">c<sub>3</sub></font> #) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="ringcat1.html#K2" target="_self">cod</a> <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# the <a href="ringcat1.html#U1" target="_self">Dom</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="ringcat1.html#U2" target="_self">Cod</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="ringcat1.html#U3" target="_self">Fun</a> of <font color="Maroon">c<sub>3</sub></font> #) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="ringcat1.html#E2:14_1_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="ringcat1.html#E13"><i><font color="Green">Lemma6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:14_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being <a href="ringcat1.html#V2" target="_self">strict</a> <a href="ringcat1.html#NM1">RingMorphism</a> st <br/>(  <a href="ringcat1.html#K1" target="_self">dom</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="ringcat1.html#K2" target="_self">cod</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>


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