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<b>let </b><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">F2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c2">V</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">f</font> being   <a href="modcat_1.html#M4" title="MODCAT_1:mode.4">Element</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K5" title="MODCAT_1:func.5">dom'</a> <font color="Olive" title="b1">f</font> ) &amp; ( for <font color="Olive" title="b1">f</font> being   <a href="modcat_1.html#M4" title="MODCAT_1:mode.4">Element</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K5" title="MODCAT_1:func.5">dom'</a> <font color="Olive" title="b1">f</font> ) implies <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:24_1_2"/><i><font color="Green" title="E14">A2</font></i>: 
for <font color="Olive" title="b1">f</font> being   <a href="modcat_1.html#M4" title="MODCAT_1:mode.4">Element</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K5" title="MODCAT_1:func.5">dom'</a> <font color="Olive" title="b1">f</font>
 <b>and </b><br/><a NAME="E2:24_1_2"/><i><font color="Green" title="E15">A3</font></i>: 
for <font color="Olive" title="b1">f</font> being   <a href="modcat_1.html#M4" title="MODCAT_1:mode.4">Element</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K5" title="MODCAT_1:func.5">dom'</a> <font color="Olive" title="b1">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="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">f</font> be    <a href="modcat_1.html#M4" title="MODCAT_1:mode.4">Element</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">f</font></span><br/><a NAME="E1:24_1_2_1"/>
<font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K5" title="MODCAT_1:func.5">dom'</a> <font color="Maroon" title="c5">f</font>
 <b>by </b><i><a class="txt" href="modcat_1.html#E1:24_1_2"><i><font color="Green" title="E14">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E2:24_1_2_1"/>
<font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">f</font>
 <b>by </b><i><a class="txt" href="modcat_1.html#E2:24_1_2"><i><font color="Green" title="E15">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/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:24_1_2"/>
<font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</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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