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<span class="kw">reconsider </span><font color="Maroon" title="c4">B</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U2</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">W1</font>, <font color="Maroon" title="c6">W2</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>; <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">A</font> being 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>  st <font color="Olive" title="b1">A</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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U2</font> holds <br/><font color="Maroon" title="c5">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Olive" title="b1">A</font> ) &amp; ( for <font color="Olive" title="b1">A</font> being 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>  st <font color="Olive" title="b1">A</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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U2</font> holds <br/><font color="Maroon" title="c6">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Olive" title="b1">A</font> ) implies <font color="Maroon" title="c5">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">W2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:41_1_2"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
for <font color="Olive" title="b1">A</font> being 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>  st <font color="Olive" title="b1">A</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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U2</font> holds <br/><font color="Maroon" title="c5">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Olive" title="b1">A</font>
 <span class="kw">and </span><br/><a NAME="E3:41_1_2"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
for <font color="Olive" title="b1">A</font> being 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>  st <font color="Olive" title="b1">A</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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U2</font> holds <br/><font color="Maroon" title="c6">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Olive" title="b1">A</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="c5">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">W2</font></span><br/>

<a NAME="E4:41_1_2"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U2</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">B</font> = <font color="Maroon" title="c4">B</font> as  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> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/>
<a NAME="E6:41_1_2"/>
<font color="Maroon" title="c5">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41_1_2"><span class="lab"><font color="Green" title="E24">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:41_1_2"/>
<font color="Maroon" title="c5">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">W2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41_1_2"><span class="lab"><font color="Green" title="E25">A2</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/>


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