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<b>let </b><font color="Maroon" title="c1">U0</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon" title="c2">U1</font> be  <a href="unialg_1.html#V3" title="UNIALG_1:attr.3">strict</a>  <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c1">U0</font>;<br/><b>let </b><font color="Maroon" title="c3">B</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font>;<br/>





<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">W</font> =  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">B</font>;<br/>
<a NAME="E2:39"/>
 <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">B</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c2">U1</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:39"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="unialg_2.html#D13" target="_self" title="UNIALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E3:39"/><b>then </b><i><font color="Green" title="E26">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">B</font></span>)</span> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">U1</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></i>;<br/>
<a NAME="E4:39"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:39"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="unialg_2.html#D13" target="_self" title="UNIALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E5:39"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E3:39"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
 <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">U1</font>
 <b>by </b><i><a class="ref" href="unialg_2.html#T15" target="_self" title="UNIALG_2:th.15">Th15</a></i>;<br/>


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