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<span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</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> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> holds <br/> ( not  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">segmental</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; not  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">segmental</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; not  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">S</font> =  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #);<br/>
<span class="kw">thus </span><a NAME="E1:26"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a> <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#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">segmental</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; not  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  )</span><br/>

<a NAME="E2:26"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">segmental</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="msualg_1.html#D12" target="_self" title="MSUALG_1:def.12">MSUALG_1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span><br/>

<span class="kw">thus </span><a NAME="E1:26_1"/>
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:26"/>
 <a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</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 class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#T9" target="_self" title="MSUALG_1:th.9">Th9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:26"/>
(  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">segmental</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; not  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">z</font></span>)</span> #) is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E9">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
