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<b>let </b><font color="Maroon" title="c1">C</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">A</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of  <a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a> <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b2">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font> holds   <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Olive" title="b2">a</font></span>)</span>,<font color="Olive" title="b1">A</font> <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></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of  <a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a> <font color="Maroon" title="c1">C</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="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font> holds   <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Olive" title="b1">a</font></span>)</span>,<font color="Maroon" title="c2">A</font> <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></span><br/><b>let </b><font color="Maroon" title="c3">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font>; <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> <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Maroon" title="c3">a</font></span>)</span>,<font color="Maroon" title="c2">A</font> <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></span><br/>





<b>thus </b> <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Maroon" title="c3">a</font></span>)</span>,<font color="Maroon" title="c2">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#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">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> <span class="p3">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pralg_2.html#T10" title="PRALG_2:th.10">PRALG_2:10</a></i>
<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#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="catalg_1.html#D5" target="_self" title="CATALG_1:def.5">Def5</a></i>
<br/>.= 
<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="card_3.html#T19" title="CARD_3:th.19">CARD_3:19</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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