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<b>consider </b><font color="Maroon" title="c3">F</font> being   <a href="ringcat1.html#NM1" title="RINGCAT1:NM.1">RingMorphism</a><b> such that </b><br/><a NAME="E2:15_1_1"/><i><font color="Green" title="E8">A2</font></i>: 
(  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> )
 <b>by </b><i><a class="txt" href="ringcat1.html#E1:15"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="ringcat1.html#D8" target="_self" title="RINGCAT1:def.8">Def8</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">S</font> =  <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(# the <a href="ringcat1.html#U1" title="RINGCAT1:sel.1">Dom</a> of <font color="Maroon" title="c3">F</font>,the <a href="ringcat1.html#U2" title="RINGCAT1:sel.2">Cod</a> of <font color="Maroon" title="c3">F</font>,the <a href="ringcat1.html#U3" title="RINGCAT1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> #);<br/>
<a NAME="E3:15_1_1"/>
(  <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(# the <a href="ringcat1.html#U1" title="RINGCAT1:sel.1">Dom</a> of <font color="Maroon" title="c3">F</font>,the <a href="ringcat1.html#U2" title="RINGCAT1:sel.2">Cod</a> of <font color="Maroon" title="c3">F</font>,the <a href="ringcat1.html#U3" title="RINGCAT1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> #) is   <a href="ringcat1.html#NM1" title="RINGCAT1:NM.1">RingMorphism</a> &amp;  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(# the <a href="ringcat1.html#U1" title="RINGCAT1:sel.1">Dom</a> of <font color="Maroon" title="c3">F</font>,the <a href="ringcat1.html#U2" title="RINGCAT1:sel.2">Cod</a> of <font color="Maroon" title="c3">F</font>,the <a href="ringcat1.html#U3" title="RINGCAT1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(# the <a href="ringcat1.html#U1" title="RINGCAT1:sel.1">Dom</a> of <font color="Maroon" title="c3">F</font>,the <a href="ringcat1.html#U2" title="RINGCAT1:sel.2">Cod</a> of <font color="Maroon" title="c3">F</font>,the <a href="ringcat1.html#U3" title="RINGCAT1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> )
 
<b>by </b><i><a class="txt" href="ringcat1.html#E2:15_1_1"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="ringcat1.html#E13"><i><font color="Green" title="E6">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:15_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being <a href="ringcat1.html#V2" title="RINGCAT1:attr.2">strict</a> <a href="ringcat1.html#NM1" title="RINGCAT1:NM.1">RingMorphism</a> st <br/>(  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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