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<b>let </b><font color="Maroon" title="c1">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:19"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c1">f</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> 
 ;<br/>

<b>set </b><font color="Maroon" title="c2">U0</font> =  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</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 class="p1">(<span class="default"><a href="pralg_1.html#K8" title="PRALG_1:func.8">TrivialOps</a> <font color="Maroon" title="c1">f</font></span>)</span> #);<br/>
<a NAME="E2:19"/><i><font color="Green" title="E15">A2</font></i>: 
( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</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 class="p1">(<span class="default"><a href="pralg_1.html#K8" title="PRALG_1:func.8">TrivialOps</a> <font color="Maroon" title="c1">f</font></span>)</span> #) is <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">homogeneous</a> &amp; the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</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 class="p1">(<span class="default"><a href="pralg_1.html#K8" title="PRALG_1:func.8">TrivialOps</a> <font color="Maroon" title="c1">f</font></span>)</span> #) is <a href="unialg_1.html#V5" title="UNIALG_1:attr.5">quasi_total</a> &amp; the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</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 class="p1">(<span class="default"><a href="pralg_1.html#K8" title="PRALG_1:func.8">TrivialOps</a> <font color="Maroon" title="c1">f</font></span>)</span> #) is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> )
 
<b>by </b><i><a class="ref" href="pralg_1.html#T10" target="_self" title="PRALG_1:th.10">Th10</a></i>;<br/>
<a NAME="E3:19"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</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 class="p1">(<span class="default"><a href="pralg_1.html#K8" title="PRALG_1:func.8">TrivialOps</a> <font color="Maroon" title="c1">f</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="ref" href="pralg_1.html#D8" target="_self" title="PRALG_1:def.8">Def8</a></i>;<br/>
<a NAME="E4:19"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</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 class="p1">(<span class="default"><a href="pralg_1.html#K8" title="PRALG_1:func.8">TrivialOps</a> <font color="Maroon" title="c1">f</font></span>)</span> #) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="pralg_1.html#E1:19"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E5:19"/><b>then </b>
the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</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 class="p1">(<span class="default"><a href="pralg_1.html#K8" title="PRALG_1:func.8">TrivialOps</a> <font color="Maroon" title="c1">f</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> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>;<br/>
<b>hence </b><a NAME="E6:19"/>
 <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</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 class="p1">(<span class="default"><a href="pralg_1.html#K8" title="PRALG_1:func.8">TrivialOps</a> <font color="Maroon" title="c1">f</font></span>)</span> #) is  <a href="unialg_1.html#V3" title="UNIALG_1:attr.3">strict</a> <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>
 <b>by </b><i><a class="txt" href="pralg_1.html#E2:19"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="unialg_1.html#D7" title="UNIALG_1:def.7">UNIALG_1:def 7</a>, <a class="ref" href="unialg_1.html#D8" title="UNIALG_1:def.8">UNIALG_1:def 8</a>, <a class="ref" href="unialg_1.html#D9" title="UNIALG_1:def.9">UNIALG_1:def 9</a></i>;<br/>


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