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<span class="kw">let </span><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> holds <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="c2">S2</font><br/> for <font color="Olive" title="b4">o1</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b5">o2</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b5">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">o1</font> holds <br/>(  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b5">o2</font>,<font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b4">o1</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b4">o1</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b5">o2</font>,<font color="Olive" title="b3">A</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> implies 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="c2">S2</font><br/> for <font color="Olive" title="b2">o1</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b3">o2</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b3">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">o1</font> holds <br/>(  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b3">o2</font>,<font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b2">o1</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b2">o1</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b3">o2</font>,<font color="Olive" title="b1">A</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:35"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c2">S2</font><br/> for <font color="Olive" title="b2">o1</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b3">o2</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b3">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">o1</font> holds <br/>(  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b3">o2</font>,<font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b2">o1</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b2">o1</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b3">o2</font>,<font color="Olive" title="b1">A</font> )</span><br/>

<a NAME="E2:35"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f</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="c1">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="pua2mss1.html#D13" title="PUA2MSS1:def.13">PUA2MSS1:def 13</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">A</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">o1</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b2">o2</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b2">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o1</font> holds <br/>(  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b2">o2</font>,<font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b1">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b1">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b2">o2</font>,<font color="Maroon" title="c5">A</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">o1</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">o2</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b1">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">o1</font> holds <br/>(  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b1">o2</font>,<font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Olive" title="b1">o2</font>,<font color="Maroon" title="c5">A</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">o2</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">o1</font> implies (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c7">o2</font>,<font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c7">o2</font>,<font color="Maroon" title="c5">A</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E3:35"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c7">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">o1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c7">o2</font>,<font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c7">o2</font>,<font color="Maroon" title="c5">A</font> )</span><br/>

<span class="kw">thus </span> <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c7">o2</font>,<font color="Maroon" title="c5">A</font> = 
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c7">o2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pralg_2.html#T10" title="PRALG_2:th.10">PRALG_2:10</a></span>
<br/>.= 
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c6">o1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="pua2mss1.html#D13" title="PUA2MSS1:def.13">PUA2MSS1:def 13</a></span>
<br/>.= 
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c6">o1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>
<br/>.= 
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c6">o1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="instalg1.html#D3" target="_self" title="INSTALG1:def.3">Def3</a></span>
<br/>.= 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pralg_2.html#T10" title="PRALG_2:th.10">PRALG_2:10</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c7">o2</font>,<font color="Maroon" title="c5">A</font></span><br/>

<a NAME="E5:35"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">g</font> <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="c1">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="pua2mss1.html#D13" title="PUA2MSS1:def.13">PUA2MSS1:def 13</a></span>;<br/>
<span class="kw">then </span> <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c7">o2</font> = 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">o1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">o1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="pua2mss1.html#D13" title="PUA2MSS1:def.13">PUA2MSS1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c6">o1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
;<br/>
<span class="kw">hence </span> <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c7">o2</font>,<font color="Maroon" title="c5">A</font> = 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c6">o1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pralg_2.html#T10" title="PRALG_2:th.10">PRALG_2:10</a></span>
<br/>.= 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c6">o1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></span>
<br/>.= 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c6">o1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="instalg1.html#D3" target="_self" title="INSTALG1:def.3">Def3</a></span>
<br/>.= 
 <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c6">o1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pralg_2.html#T10" title="PRALG_2:th.10">PRALG_2:10</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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