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<span class="kw">let </span><font color="Maroon" title="c2">T</font> be    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">T</font> is  <a href="instalg1.html#V1" title="INSTALG1:attr.1">feasible</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">f</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">g</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font>;<br/>
<a NAME="E1:15_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></span>;<br/>
<a NAME="E2:15_1_1"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>, <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="instalg1.html#D2" target="_self" title="INSTALG1:def.2">Def2</a></span>;<br/>
<a NAME="E3:15_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pua2mss1.html#D12" title="PUA2MSS1:def.12">PUA2MSS1:def 12</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:15_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="instalg1.html#D1" target="_self" title="INSTALG1:def.1">INSTALG1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E5:15_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A3</font></span>: 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15_1_1"><span class="lab"><font color="Green" title="E12">A2</font></span></a></span>;<br/>
<a NAME="E6:15_1_1"/>
(  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="instalg1.html#T7" target="_self" title="INSTALG1:th.7">Th8</a>, <a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:15_1_1"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_1_1"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E1:15_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="instalg1.html#T10" target="_self" title="INSTALG1:th.10">Th11</a>, <a class="ref" href="relat_1.html#T27" title="RELAT_1:th.27">RELAT_1:27</a>, <a class="ref" href="relat_1.html#T38" title="RELAT_1:th.38">RELAT_1:38</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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