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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>; <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> being   <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</a> of <font color="Maroon" title="c1">U0</font><br/> for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being  <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="b2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Olive" title="b3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">A</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="Olive" title="b1">U1</font> holds <br/><span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Olive" title="b1">U1</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="b3">B</font></span><br/><b>let </b><font color="Maroon" title="c2">U1</font> be    <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"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <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#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</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="c2">U1</font> holds <br/><span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c2">U1</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="b2">B</font></span><br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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"> ( ( <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</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="c2">U1</font> implies <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c2">U1</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="c4">B</font> )</span><br/>





<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E26">A1</font></i>: 
( ( <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</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="c2">U1</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"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c2">U1</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="c4">B</font></span><br/>

<a NAME="E2:41"/><b>then </b><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c3">A</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">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D13" target="_self" title="UNIALG_2:def.13">Def13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">u1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font>, <font color="Maroon" title="c6">a</font> = 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">A</font></span>)</span> 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="c7">b</font> = <font color="Maroon" title="c6">a</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">u1</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="E5:41"/><i><font color="Green" title="E28">A3</font></i>: 
<span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c2">U1</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>
 
<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="E6:41"/><b>then </b><i><font color="Green" title="E29">A4</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">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"><span class="p2">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c2">U1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D13" target="_self" title="UNIALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E7:41"/>
<font color="Maroon" title="c3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">u1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">a</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">u1</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E2:41"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="xboole_1.html#T13" title="XBOOLE_1:th.13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E8:41"/><b>then </b>
<font color="Maroon" title="c4">B</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"><span class="p2">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c2">U1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:41"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="unialg_2.html#E6:41"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E9:41"/><b>then </b><i><font color="Green" title="E30">A5</font></i>: 
 <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font> is  <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c2">U1</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:41"><i><font color="Green" title="E26">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="E10:41"/>
( <font color="Maroon" title="c4">B</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="c4">B</font></span>)</span> &amp; <font color="Maroon" title="c5">u1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> )
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:41"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="unialg_2.html#D13" target="_self" title="UNIALG_2:def.13">Def13</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E11:41"/><b>then </b><i><font color="Green" title="E31">A6</font></i>: 
( <font color="Maroon" title="c5">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="c4">B</font></span>)</span> &amp; <font color="Maroon" title="c3">A</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="c4">B</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E12:41"/><b>then </b><i><font color="Green" title="E32">A7</font></i>: 
<font color="Maroon" title="c3">A</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">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E2:41"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1"/>
( <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span><b>by </b><i><a class="txt" href="unialg_2.html#E1:41"><i><font color="Green" title="E26">A1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1"><b>case </b></a><a NAME="E1:41_1_1_1"/>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><div class="add"><b>hence </b><a NAME="E2:41_1_1_1"/>
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">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:41"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="unialg_2.html#E11:41"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_2"><b>case </b></a><a NAME="E1:41_1_1_2"/><i><font color="Green" title="E33">A8</font></i>: 
 <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><div class="add"><a NAME="E2:41_1_1_2"/>
(  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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">A</font></span>)</span> &amp;  <a href="unialg_2.html#K6" title="UNIALG_2:func.6">Constants</a> <font color="Maroon" title="c1">U0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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="c4">B</font></span>)</span> )
 <b>by </b><i><a class="ref" href="unialg_2.html#T18" target="_self" title="UNIALG_2:th.18">Th18</a></i>;<br/><b>hence </b><a NAME="E3:41_1_1_2"/>
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">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="unialg_2.html#E1:41_1_1_2"><i><font color="Green" title="E33">A8</font></i></a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E14:41"/><b>then </b>
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">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E15:41"/><b>then </b><i><font color="Green" title="E33">A9</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <span class="p2">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <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">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span>
 
<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="E16:41"/><b>then </b>
 <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font> is    <a href="unialg_2.html#M3" title="UNIALG_2:mode.3">SubAlgebra</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">A</font></span>)</span> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:41"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="unialg_2.html#E12:41"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="unialg_2.html#D13" target="_self" title="UNIALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E17:41"/><b>then </b><i><font color="Green" title="E34">A10</font></i>: 
<font color="Maroon" title="c6">a</font> 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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K5" title="UNIALG_2:func.5">/\</a> <span class="p2">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span>
 
<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="E18:41"/>
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">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E19:41"/><b>then </b>
<font color="Maroon" title="c6">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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E15:41"><i><font color="Green" title="E33">A9</font></i></a>, <a class="txt" href="unialg_2.html#E17:41"><i><font color="Green" title="E34">A10</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E20:41"/><b>then </b>
<font color="Maroon" title="c6">a</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="c4">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E21:41"/><b>then </b>
<font color="Maroon" title="c7">b</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="c4">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E11:41"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E22:41"/><b>then </b>
 <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c7">b</font> is  <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  <a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D13" target="_self" title="UNIALG_2:def.13">Def13</a></i>;<br/>
<b>hence </b><a NAME="E23:41"/>
<span class="p1">(<span class="default"><a href="unialg_2.html#K7" title="UNIALG_2:func.7">GenUnivAlg</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="unialg_2.html#K8" title="UNIALG_2:func.8">"\/"</a> <font color="Maroon" title="c2">U1</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="c4">B</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E5:41"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="unialg_2.html#E9:41"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="unialg_2.html#T13" target="_self" title="UNIALG_2:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
