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<b>let </b><font color="Maroon" title="c1">F</font> be  <a href="ringcat1.html#V2" title="RINGCAT1:attr.2">strict</a> <a href="ringcat1.html#NM1" title="RINGCAT1:NM.1">RingMorphism</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H</font> being  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a> ex <font color="Olive" title="b3">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">H</font> st <br/>( <font color="Maroon" title="c1">F</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">H</font> &amp; <font color="Maroon" title="c1">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="Olive" title="b1">G</font>,<font color="Olive" title="b2">H</font>,<font color="Olive" title="b3">f</font> #) &amp; <font color="Olive" title="b3">f</font> is <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )</span><br/>

<b>consider </b><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">H</font> being   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a><b> such that </b><br/><a NAME="E2:26"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c2">G</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Maroon" title="c3">H</font>
 <b>and </b><br/><a NAME="E3:26"/>
(  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> )
 <b>and </b><br/><a NAME="E4:26"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c1">F</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="ringcat1.html#E18"><i><font color="Green" title="E11">Lm6</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">F'</font> = <font color="Maroon" title="c1">F</font> as    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> <b>by </b><i><a class="txt" href="#E4:26"><i><font color="Green" title="E17">A2</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font><b> such that </b><br/><a NAME="E7:26"/><i><font color="Green" title="E18">A3</font></i>: 
( <font color="Maroon" title="c4">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="c2">G</font>,<font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c5">f</font> #) &amp; <font color="Maroon" title="c5">f</font> is <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )
 <b>by </b><i><a class="txt" href="#E2:26"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ringcat1.html#E22"><i><font color="Green" title="E14">Lm7</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">G</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">H</font> being  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a> ex <font color="Olive" title="b2">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">G</font>,<font color="Olive" title="b1">H</font> st <br/>( <font color="Maroon" title="c1">F</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Olive" title="b1">H</font> &amp; <font color="Maroon" title="c1">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="c2">G</font>,<font color="Olive" title="b1">H</font>,<font color="Olive" title="b2">f</font> #) &amp; <font color="Olive" title="b2">f</font> is <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )</span><br/>

<b>take </b>
<font color="Maroon" title="c3">H</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> st <br/>( <font color="Maroon" title="c1">F</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c1">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="c2">G</font>,<font color="Maroon" title="c3">H</font>,<font color="Olive" title="b1">f</font> #) &amp; <font color="Olive" title="b1">f</font> is <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )</span><br/>

<b>take </b>
<font color="Maroon" title="c5">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c1">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="c2">G</font>,<font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c5">f</font> #) &amp; <font color="Maroon" title="c5">f</font> is <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )</span><br/>

<b>thus </b><a NAME="E8:26"/>
( <font color="Maroon" title="c1">F</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c1">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="c2">G</font>,<font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c5">f</font> #) &amp; <font color="Maroon" title="c5">f</font> is <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )
 <b>by </b><i><a class="txt" href="#E7:26"><i><font color="Green" title="E18">A3</font></i></a></i>; <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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