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<span class="kw">let </span><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>,<span class="p1">(<span class="default"><a href="grcat_1.html#K19" title="GRCAT_1:func.19">Morphs</a> <font color="Maroon" title="c1">V</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:95_3_2"/><span class="lab"><font color="Green" title="E38">A8</font></span>: 
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>
 <span class="kw">and </span><br/><a NAME="E2:95_3_2"/><span class="lab"><font color="Green" title="E39">A9</font></span>: 
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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="95_3_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E1:95_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95_3_2"><span class="lab"><font color="Green" title="E38">A8</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E2:95_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:95_3_2"><span class="lab"><font color="Green" title="E39">A9</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:95_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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