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<b>let </b><font color="Maroon" title="c1">S1</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="instalg1.html#V1" title="INSTALG1:attr.1">feasible</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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">S2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b2">S3</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Olive" title="b1">S2</font><br/> for <font color="Olive" title="b3">A</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font> holds  <font color="Olive" title="b3">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Olive" title="b2">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Olive" title="b1">S2</font></span>)</span> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Olive" title="b2">S3</font></span><br/><b>let </b><font color="Maroon" title="c2">S2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c1">S1</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">S3</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c2">S2</font><br/> for <font color="Olive" title="b2">A</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font> holds  <font color="Olive" title="b2">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Olive" title="b1">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Olive" title="b1">S3</font></span><br/><b>let </b><font color="Maroon" title="c3">S3</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c2">S2</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> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font> holds  <font color="Olive" title="b1">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c3">S3</font></span><br/><b>let </b><font color="Maroon" title="c4">A</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c3">S3</font></span><br/>







<b>set </b><font color="Maroon" title="c5">f1</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">S2</font>;<br/>
<b>set </b><font color="Maroon" title="c6">g1</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">S2</font>;<br/>
<b>set </b><font color="Maroon" title="c7">f2</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="c3">S3</font>;<br/>
<b>set </b><font color="Maroon" title="c8">g2</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="c3">S3</font>;<br/>
<a NAME="E1:37"/>
(  <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#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</font></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 <font color="Maroon" title="c3">S3</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="c3">S3</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="c3">S3</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</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 <font color="Maroon" title="c2">S2</font> &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">S3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="instalg1.html#T11" target="_self" title="INSTALG1:th.11">Th11</a>, <a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>;<br/>
<a NAME="E2:37"/><b>then </b><i><font color="Green" title="E21">A1</font></i>: 
( <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">S2</font></span>)</span> <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#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">S3</font> &amp; <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">S2</font></span>)</span> <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="c3">S3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">S3</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T79" title="RELAT_1:th.79">RELAT_1:79</a></i>;<br/>
<a NAME="E3:37"/>
(  <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">S2</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">S2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c1">S1</font> &amp;  <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="c3">S3</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="c3">S3</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c3">S3</font>,<font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="instalg1.html#D2" target="_self" title="INSTALG1:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E4:37"/>
<font color="Maroon" title="c4">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="instalg1.html#K2" title="INSTALG1:func.2">|</a> <font color="Maroon" title="c3">S3</font>
 <b>by </b><i><a class="txt" href="#E2:37"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="instalg1.html#T28" target="_self" title="INSTALG1:th.28">Th28</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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