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<b>let </b><font color="Maroon">F1</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12">UnSubAlLattice</a> <font color="Maroon">U01</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12">UnSubAlLattice</a> <font color="Maroon">U02</font></span>)</span>, <font color="Maroon">F2</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12">UnSubAlLattice</a> <font color="Maroon">U01</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12">UnSubAlLattice</a> <font color="Maroon">U02</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:33_1_2"/><i><font color="Green">E47</font></i>: 
for <font color="Olive">U1</font> being <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">U01</font><br/> for <font color="Olive">H</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U02</font>  st <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">U1</font> holds <br/><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">U1</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K7">GenUnivAlg</a> <font color="Olive">H</font>
 <b>and </b><br/><a NAME="E2:33_1_2"/><i><font color="Green">E48</font></i>: 
for <font color="Olive">U1</font> being <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">U01</font><br/> for <font color="Olive">H</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U02</font>  st <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">U1</font> holds <br/><font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">U1</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K7">GenUnivAlg</a> <font color="Olive">H</font>
 ;<br/>

<a NAME="E3:33_1_2"/>
for <font color="Olive">l</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">l</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12">UnSubAlLattice</a> <font color="Maroon">U01</font></span>)</span> holds <br/><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">l</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">l</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:33_1_2_1"/>
<font color="Maroon">l</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12">UnSubAlLattice</a> <font color="Maroon">U01</font></span>)</span>
 ;<br/>

<a NAME="E2:33_1_2_1"/><b>then </b>
<font color="Maroon">l</font> is    <a href="unialg_3.html#M2" target="_self">Element</a> of  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U01</font>
 
;<br/>
<b>then consider </b><font color="Maroon">U1</font> being  <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">U01</font><b> such that </b><br/><a NAME="E4:33_1_2_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">U1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">H</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U02</font><b> such that </b><br/><a NAME="E6:33_1_2_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>
 ;<br/>
<a NAME="E7:33_1_2_1"/>
<font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K7">GenUnivAlg</a> <font color="Maroon">H</font>
 
<b>by </b><i>, <a class="ref" href="unialg_3.html#D1" target="_self">Def1</a>, </i>;<br/>
<b>hence </b><a NAME="E8:33_1_2_1"/>
<font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
 <b>by </b><i>, <a class="ref" href="unialg_3.html#D1" target="_self">Def1</a>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:33_1_2"/>
<font color="Maroon">F1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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