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<b>let </b><font color="Maroon" title="c1">I</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">S</font> being 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> <br/> for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b3">A</font> being   <a href="pralg_2.html#M2" title="PRALG_2:mode.2">MSAlgebra-Family</a> of <font color="Maroon" title="c1">I</font>,<font color="Olive" title="b1">S</font> holds   <a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Olive" title="b3">A</font>,<font color="Olive" title="b2">i</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Olive" title="b3">A</font>,<font color="Olive" title="b3">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Olive" title="b2">i</font></span><br/><b>let </b><font color="Maroon" title="c2">S</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b2">A</font> being   <a href="pralg_2.html#M2" title="PRALG_2:mode.2">MSAlgebra-Family</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">S</font> holds   <a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">i</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Olive" title="b2">A</font>,<font color="Olive" title="b2">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Olive" title="b1">i</font></span><br/><b>let </b><font color="Maroon" title="c3">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</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="pralg_2.html#M2" title="PRALG_2:mode.2">MSAlgebra-Family</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">S</font> holds   <a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Olive" title="b1">A</font>,<font color="Maroon" title="c3">i</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b1">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span><br/><b>let </b><font color="Maroon" title="c4">A</font> be    <a href="pralg_2.html#M2" title="PRALG_2:mode.2">MSAlgebra-Family</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span><br/>







<b>thus </b><a NAME="E1:31"/>
 <a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_3.html#D9" title="MSUALG_3:def.9">MSUALG_3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:31_1"/>
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span>; <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"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">x</font></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c7">F</font> =  <a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font>;<br/>
<b>set </b><font color="Maroon" title="c8">s</font> =  <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c5">o</font>;<br/>
<a NAME="E2:31_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S</font>
 
;<br/>
<a NAME="E3:31_1"/><b>then </b><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<i><font color="Green" title="E25">A2</font></i>:  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> = 
<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"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">o</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D10" title="MSUALG_1:def.10">MSUALG_1:def 10</a></i>
<br/>.= 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">o</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:31_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pralg_2.html#K10" title="PRALG_2:func.10">SORTS</a> <font color="Maroon" title="c4">A</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="c5">o</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D7" title="MSUALG_1:def.7">MSUALG_1:def 7</a></i>
<br/>.= 
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K9" title="PRALG_2:func.9">Carrier</a> <font color="Maroon" title="c4">A</font>,<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="c5">o</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pralg_2.html#D17" title="PRALG_2:def.17">PRALG_2:def 17</a></i>
;<br/>
<b>thus </b><a NAME="E5:31_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K6" title="MSUALG_3:func.6">#</a> <font color="Maroon" title="c6">x</font></span>)</span>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_2_1"/>
(  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</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>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_2_1_1"><b>suppose </b></a><a NAME="E1:31_1_2_1_1"/><i><font color="Green" title="E26">A3</font></i>: 
 <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K6" title="MSUALG_3:func.6">#</a> <font color="Maroon" title="c6">x</font></span>)</span></span><br/><div class="add"><a NAME="E2:31_1_2_1_1"/><b>then </b><i><font color="Green" title="E27">A4</font></i>: 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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="ref" href="pralg_2.html#T11" title="PRALG_2:th.11">PRALG_2:11</a></i>;<br/><a NAME="E3:31_1_2_1_1"/><b>then </b><i><font color="Green" title="E28">A5</font></i>: 
<font color="Maroon" title="c6">x</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="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E4:31_1_2_1_1"/>
 <a href="pralg_3.html#K2" title="PRALG_3:func.2">const</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K9" title="PRALG_2:func.9">Carrier</a> <font color="Maroon" title="c4">A</font>,<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="c5">o</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:31_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="#E1:31_1_2_1_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="pralg_3.html#T6" target="_self" title="PRALG_3:th.6">Th6</a></i>;<br/><a NAME="E5:31_1_2_1_1"/><b>then </b><i><font color="Green" title="E29">A6</font></i>: 
 <a href="pralg_3.html#K2" title="PRALG_3:func.2">const</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K3" title="PRALG_3:func.3">proj</a> <span class="p2">(<span class="default"><a href="pralg_2.html#K9" title="PRALG_2:func.9">Carrier</a> <font color="Maroon" title="c4">A</font>,<span class="p3">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c5">o</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="pralg_3.html#D2" target="_self" title="PRALG_3:def.2">Def2</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K2" title="PRALG_3:func.2">const</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:31_1_2_1_1"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pralg_3.html#K3" title="PRALG_3:func.3">proj</a> <span class="p2">(<span class="default"><a href="pralg_2.html#K9" title="PRALG_2:func.9">Carrier</a> <font color="Maroon" title="c4">A</font>,<span class="p3">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c5">o</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K2" title="PRALG_3:func.2">const</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pralg_3.html#D3" target="_self" title="PRALG_3:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pralg_3.html#K2" title="PRALG_3:func.2">const</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
<b>by </b><i><a class="txt" href="#E5:31_1_2_1_1"><i><font color="Green" title="E29">A6</font></i></a>, <a class="ref" href="pralg_3.html#D2" target="_self" title="PRALG_3:def.2">Def2</a></i>
<br/>.= 
 <a href="pralg_3.html#K2" title="PRALG_3:func.2">const</a> <font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31_1_2_1_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="pralg_3.html#T10" target="_self" title="PRALG_3:th.10">Th10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K6" title="MSUALG_3:func.6">#</a> <font color="Maroon" title="c6">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31_1_2_1_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="#E3:31_1_2_1_1"><i><font color="Green" title="E28">A5</font></i></a>, <a class="ref" href="pralg_3.html#T12" target="_self" title="PRALG_3:th.12">Th12</a></i>
;<br/><b>hence </b><a NAME="E7:31_1_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K6" title="MSUALG_3:func.6">#</a> <font color="Maroon" title="c6">x</font></span>)</span>
 ; <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="31_1_2_1_2"><b>suppose </b></a><a NAME="E1:31_1_2_1_2"/><i><font color="Green" title="E26">A7</font></i>: 
 <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K6" title="MSUALG_3:func.6">#</a> <font color="Maroon" title="c6">x</font></span>)</span></span><br/><div class="add"><a NAME="E2:31_1_2_1_2"/>
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K9" title="PRALG_2:func.9">Carrier</a> <font color="Maroon" title="c4">A</font>,<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="c5">o</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:31_1"><i><font color="Green" title="E25">A2</font></i></a></i>;<br/><a NAME="E3:31_1_2_1_2"/><b>then </b><i><font color="Green" title="E27">A8</font></i>: 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K3" title="PRALG_3:func.3">proj</a> <span class="p2">(<span class="default"><a href="pralg_2.html#K9" title="PRALG_2:func.9">Carrier</a> <font color="Maroon" title="c4">A</font>,<span class="p3">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c5">o</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="pralg_3.html#D2" target="_self" title="PRALG_3:def.2">Def2</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">D</font> = <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <b>by </b><i><a class="txt" href="#E4:31_1"><i><font color="Green" title="E25">A2</font></i></a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="pralg_3.html#K3" title="PRALG_3:func.3">proj</a> <span class="p2">(<span class="default"><a href="pralg_2.html#K9" title="PRALG_2:func.9">Carrier</a> <font color="Maroon" title="c4">A</font>,<span class="p3">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c5">o</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font></span>)</span>
<b>by </b><i><a class="ref" href="pralg_3.html#D3" target="_self" title="PRALG_3:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c9">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
<b>by </b><i><a class="txt" href="#E3:31_1_2_1_2"><i><font color="Green" title="E27">A8</font></i></a>, <a class="ref" href="pralg_3.html#D2" target="_self" title="PRALG_3:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_6.html#K10" title="FUNCT_6:func.10">commute</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31_1_2_1_2"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="pralg_3.html#T23" target="_self" title="PRALG_3:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K6" title="MSUALG_3:func.6">#</a> <font color="Maroon" title="c6">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31_1_2_1_2"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="pralg_3.html#T24" target="_self" title="PRALG_3:th.24">Th24</a></i>
;<br/><b>hence </b><a NAME="E6:31_1_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3: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="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p3">(<span class="default"><a href="pralg_2.html#K14" title="PRALG_2:func.14">product</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_3.html#K4" title="PRALG_3:func.4">proj</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="msualg_3.html#K6" title="MSUALG_3:func.6">#</a> <font color="Maroon" title="c6">x</font></span>)</span>
 ; <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>


</div><b>end;</b></div>


</div>
