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<span class="kw">let </span><font color="Maroon" title="c3">g1</font>, <font color="Maroon" title="c4">g2</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c1">H</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  &amp; <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">g2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  implies <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:105_1_2"/><span class="lab"><font color="Green" title="E67">A2</font></span>: 
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> 
 <span class="kw">and </span><br/><a NAME="E2:105_1_2"/><span class="lab"><font color="Green" title="E68">A3</font></span>: 
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">g2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span><br/><a NAME="E1:105_1_2_1"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="waybel_1.html#R4" title="WAYBEL_1:pred.4">is_maximum_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c5">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:105"><span class="lab"><font color="Green" title="E66">A1</font></span></a>, <a class="txt" href="#E1:105_1_2"><span class="lab"><font color="Green" title="E67">A2</font></span></a>, <a class="ref" href="waybel_1.html#T11" target="_self" title="WAYBEL_1:th.11">Th12</a></span>;<br/><a NAME="E2:105_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A4</font></span>: 
<font color="Maroon" title="c3">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">H</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_1.html#D7" target="_self" title="WAYBEL_1:def.7">Def7</a></span>;<br/><a NAME="E3:105_1_2_1"/>
<font color="Maroon" title="c4">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="waybel_1.html#R4" title="WAYBEL_1:pred.4">is_maximum_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c5">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:105"><span class="lab"><font color="Green" title="E66">A1</font></span></a>, <a class="txt" href="#E2:105_1_2"><span class="lab"><font color="Green" title="E68">A3</font></span></a>, <a class="ref" href="waybel_1.html#T11" target="_self" title="WAYBEL_1:th.11">Th12</a></span>;<br/><span class="kw">hence </span><a NAME="E4:105_1_2_1"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:105_1_2_1"><span class="lab"><font color="Green" title="E69">A4</font></span></a>, <a class="ref" href="waybel_1.html#D7" target="_self" title="WAYBEL_1:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:105_1_2"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" title="FUNCT_2:th.63">FUNCT_2:63</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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