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<b>let </b><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:18_1_2"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c1">C1</font> is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> &amp; <font color="Maroon" title="c1">C1</font> is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> )
 <b>and </b><br/><a NAME="E2:18_1_2"/><i><font color="Green" title="E12">A2</font></i>: 
( <font color="Maroon" title="c2">C2</font> is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> &amp; <font color="Maroon" title="c2">C2</font> is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> )
 ;<br/>

<a NAME="E3:18_1_2"/>
<font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:18_1_2_1"/><i><font color="Green" title="E13">A3</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="msalimit.html#E1:18_1_2"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="msalimit.html#E2:18_1_2"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>
<a NAME="E2:18_1_2_1"/><i><font color="Green" title="E14">A4</font></i>: 
( the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="msalimit.html#E1:18_1_2"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="msalimit.html#E2:18_1_2"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="msualg_1.html#D5" title="MSUALG_1:def.5">MSUALG_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">RS</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c4">RT</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c2">C2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> , <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <b>by </b><i><a class="txt" href="msalimit.html#E1:18_1_2_1"><i><font color="Green" title="E13">A3</font></i></a></i>;<br/>
<a NAME="E4:18_1_2_1"/><i><font color="Green" title="E15">A5</font></i>: 
( <font color="Maroon" title="c3">RS</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c4">RT</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="ref" href="altcat_1.html#T3" title="ALTCAT_1:th.3">ALTCAT_1:3</a>, <a class="ref" href="funct_2.html#T12" title="FUNCT_2:th.12">FUNCT_2:12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">A</font> = the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c6">B</font> = the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c2">C2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <b>by </b><i><a class="txt" href="msalimit.html#E1:18_1_2_1"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="msalimit.html#E2:18_1_2_1"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="funct_7.html#T19" title="FUNCT_7:th.19">FUNCT_7:19</a></i>;<br/>
<a NAME="E6:18_1_2_1"/><i><font color="Green" title="E16">A6</font></i>: 
<font color="Maroon" title="c5">A</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">B</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T66" title="FUNCT_2:th.66">FUNCT_2:66</a></i>;<br/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C1</font> = 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="msalimit.html#E4:18_1_2_1"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>
<br/>.= 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c2">C2</font>
<b>by </b><i><a class="txt" href="msalimit.html#E4:18_1_2_1"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E8:18_1_2_1"/>
<font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C2</font>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:18_1_2_1"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="msalimit.html#E2:18_1_2_1"><i><font color="Green" title="E14">A4</font></i></a>, <a class="txt" href="msalimit.html#E6:18_1_2_1"><i><font color="Green" title="E16">A6</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:18_1_2"/>
<font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C2</font>
 ;<br/>


</div>
