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<b>let </b><font color="Maroon" title="c1">U0</font> be  <a href="unialg_2.html#V2" title="UNIALG_2:attr.2">with_const_op</a> <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">U1</font>, <font color="Olive" title="b2">U2</font> being <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> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">U1</font> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <font color="Olive" title="b2">U2</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Olive" title="b2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">U2</font></span><br/><b>let </b><font color="Maroon" title="c2">U1</font>, <font color="Maroon" title="c3">U2</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">U1</font> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <font color="Maroon" title="c3">U2</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c3">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">U2</font></span><br/>



<b>reconsider </b><font color="Maroon" title="c4">u12</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">U1</font> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <font color="Maroon" title="c3">U2</font></span>)</span>, <font color="Maroon" title="c5">u2</font> = 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="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self" title="UNIALG_2:def.8">Def8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">A</font> = <font color="Maroon" title="c4">u12</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">u2</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> ;<br/>
<a NAME="E3:44"/><i><font color="Green" title="E29">A1</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">U1</font> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <font color="Maroon" title="c3">U2</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c3">U2</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="c6">A</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D14" target="_self" title="UNIALG_2:def.14">Def14</a></i>;<br/>
<a NAME="E4:44"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U2</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#T20" target="_self" title="UNIALG_2:th.20">Th20</a></i>;<br/>
<a NAME="E5:44"/><b>then </b>
<font color="Maroon" title="c4">u12</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#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">U2</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D10" target="_self" title="UNIALG_2:def.10">Def10</a></i>;<br/>
<a NAME="E6:44"/><b>then </b>
<font color="Maroon" title="c4">u12</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">u2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E7:44"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">U1</font> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <font color="Maroon" title="c3">U2</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c3">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">U2</font>
 <b>by </b><i><a class="txt" href="#E3:44"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="unialg_2.html#T22" target="_self" title="UNIALG_2:th.22">Th22</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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