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<b>let </b><font color="Maroon" title="c2">F1</font>, <font color="Maroon" title="c3">F2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">V</font>, <a href="grcat_1.html#K19" title="GRCAT_1:func.19">Morphs</a> <font color="Maroon" title="c1">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">G</font> being   <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Maroon" title="c2">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Olive" title="b1">G</font> ) &amp; ( for <font color="Olive" title="b1">G</font> being   <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Maroon" title="c3">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Olive" title="b1">G</font> ) implies <font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:84_3_2"/><i><font color="Green" title="E43">A8</font></i>: 
for <font color="Olive" title="b1">G</font> being   <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Maroon" title="c2">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Olive" title="b1">G</font>
 <b>and </b><br/><a NAME="E2:84_3_2"/><i><font color="Green" title="E44">A9</font></i>: 
for <font color="Olive" title="b1">G</font> being   <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Maroon" title="c3">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Olive" title="b1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_3_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">G</font> be    <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of <font color="Maroon" title="c1">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="c2">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">G</font></span><br/><a NAME="E1:84_3_2_1"/>
<font color="Maroon" title="c2">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="txt" href="grcat_1.html#E1:84_3_2"><i><font color="Green" title="E43">A8</font></i></a></i>;<br/><b>hence </b><a NAME="E2:84_3_2_1"/>
<font color="Maroon" title="c2">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="txt" href="grcat_1.html#E2:84_3_2"><i><font color="Green" title="E44">A9</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="E4:84_3_2"/>
<font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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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