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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b3">m</font>, <font color="Olive" title="b4">m'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>  st <font color="Olive" title="b3">m</font> is <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> &amp; <font color="Olive" title="b4">m'</font> is <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> &amp;  ex <font color="Olive" title="b5">O</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font> st <font color="Olive" title="b5">O</font> is <a href="altcat_3.html#V8" title="ALTCAT_3:attr.8">_zero</a> holds <br/><font color="Olive" title="b3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">m'</font></span><br/><b>let </b><font color="Maroon" title="c2">o1</font>, <font color="Maroon" title="c3">o2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">m'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font>  st <font color="Olive" title="b1">m</font> is <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> &amp; <font color="Olive" title="b2">m'</font> is <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> &amp;  ex <font color="Olive" title="b3">O</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font> st <font color="Olive" title="b3">O</font> is <a href="altcat_3.html#V8" title="ALTCAT_3:attr.8">_zero</a> holds <br/><font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">m'</font></span><br/><b>let </b><font color="Maroon" title="c4">m</font>, <font color="Maroon" title="c5">m'</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">m</font> is <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> &amp; <font color="Maroon" title="c5">m'</font> is <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a> &amp;  ex <font color="Olive" title="b1">O</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font> st <font color="Olive" title="b1">O</font> is <a href="altcat_3.html#V8" title="ALTCAT_3:attr.8">_zero</a> implies <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m'</font> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:10"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c4">m</font> is <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>
 <b>and </b><br/><a NAME="E2:10"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c5">m'</font> is <a href="altcat_3.html#V9" title="ALTCAT_3:attr.9">_zero</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( for <font color="Olive" title="b1">O</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>  holds not <font color="Olive" title="b1">O</font> is <a href="altcat_3.html#V8" title="ALTCAT_3:attr.8">_zero</a> or <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m'</font> )</span><br/>

<b>given </b><font color="Maroon" title="c6">O</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font><b> such that </b><a NAME="E4:10"/><i><font color="Green" title="E7">A3</font></i>: 
<font color="Maroon" title="c6">O</font> is <a href="altcat_3.html#V8" title="ALTCAT_3:attr.8">_zero</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m'</font></span><br/>

<b>consider </b><font color="Maroon" title="c7">a</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c6">O</font>;<br/>
<b>consider </b><font color="Maroon" title="c8">b</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c6">O</font>,<font color="Maroon" title="c3">o2</font>;<br/>
<b>consider </b><font color="Maroon" title="c9">n</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c6">O</font>,<font color="Maroon" title="c6">O</font>;<br/>
<b>thus </b><font color="Maroon" title="c4">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">b</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:10"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="altcat_4.html#E4:10"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="altcat_3.html#D12" title="ALTCAT_3:def.12">ALTCAT_3:def 12</a></i>
<br/>.= 
<font color="Maroon" title="c5">m'</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E2:10"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="altcat_4.html#E4:10"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="altcat_3.html#D12" title="ALTCAT_3:def.12">ALTCAT_3:def 12</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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