<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><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> ; <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="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>  implies  <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> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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></span><br/>

<span class="kw">set </span><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"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
( 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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pralg_1.html#T10" target="_self" title="PRALG_1:th.10">Th10</a></span>;<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pralg_1.html#D8" target="_self" title="PRALG_1:def.8">Def8</a></span>;<br/>
<a NAME="E4:19"/><span class="kw">then </span>
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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E13">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:19"/>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E14">A2</font></span></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></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>
