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

<b>consider </b><font color="Maroon" title="c2">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">f</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">a</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,<font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="unialg_1.html#T2" target="_self" title="UNIALG_1:th.2">Th2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c3">f</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span>,<font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="partfun1.html#T119" title="PARTFUN1:th.119">PARTFUN1:119</a></i>;<br/>
<b>take </b>
<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">homogeneous</a> &amp; <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="unialg_1.html#V5" title="UNIALG_1:attr.5">quasi_total</a> &amp; <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> )</span><br/>

<b>thus </b><a NAME="E4:17_1_1"/>
<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">homogeneous</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="unialg_1.html#V5" title="UNIALG_1:attr.5">quasi_total</a> &amp; <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_1.html#D4" target="_self" title="UNIALG_1:def.4">UNIALG_1:def 4</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">h</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,<font color="Maroon" title="c1">A</font>  st <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> &amp; <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> holds <br/><font color="Olive" title="b1">h</font> is <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a></span><br/><b>let </b><font color="Maroon" title="c6">h</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,<font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> &amp; <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> implies <font color="Maroon" title="c6">h</font> is <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> )</span><br/>



<b>assume </b><a NAME="E1:17_1_1_1"/><i><font color="Green" title="E6">A1</font></i>: 
( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> &amp; <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">h</font> is <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a></span><br/>

<a NAME="E2:17_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/>
<a NAME="E3:17_1_1_1"/><b>then </b>
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 
<b>by </b><i><a class="txt" href="unialg_1.html#E1:17_1_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:17_1_1_1"/><b>then </b>
( <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c4">f</font> is  <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,<font color="Maroon" title="c1">A</font> )
 
<b>by </b><i><a class="ref" href="unialg_1.html#T2" target="_self" title="UNIALG_1:th.2">Th2</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E5:17_1_1_1"/>
<font color="Maroon" title="c6">h</font> is <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a>
 ; <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>

<b>thus </b><a NAME="E5:17_1_1"/>
<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="unialg_1.html#V5" title="UNIALG_1:attr.5">quasi_total</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_1.html#D5" target="_self" title="UNIALG_1:def.5">UNIALG_1:def 5</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">h</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,<font color="Maroon" title="c1">A</font>  st <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> &amp; <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> holds <br/><font color="Olive" title="b1">h</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a></span><br/><b>let </b><font color="Maroon" title="c6">h</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,<font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> &amp; <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> implies <font color="Maroon" title="c6">h</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> )</span><br/>



<b>assume </b><a NAME="E1:17_1_1_2"/><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> &amp; <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">h</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a></span><br/>

<a NAME="E2:17_1_1_2"/><b>then </b>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/>
<a NAME="E3:17_1_1_2"/><b>then </b>
<font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 
<b>by </b><i><a class="txt" href="unialg_1.html#E1:17_1_1_2"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:17_1_1_2"/><b>then </b>
( <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c4">f</font> is  <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,<font color="Maroon" title="c1">A</font> )
 
<b>by </b><i><a class="ref" href="unialg_1.html#T2" target="_self" title="UNIALG_1:th.2">Th2</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E5:17_1_1_2"/>
<font color="Maroon" title="c6">h</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a>
 ; <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>

<b>thus </b><a NAME="E6:17_1_1"/>
<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>
  <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="17_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">n</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"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> or  not <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<b>assume </b><a NAME="E1:17_1_1_3"/><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">n</font> = <font color="Maroon" title="c5">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E3:17_1_1_3"/>
<font color="Maroon" title="c6">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="unialg_1.html#E1:17_1_1_3"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/>
<a NAME="E4:17_1_1_3"/><b>then </b>
<font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:17_1_1_3"/>
not <span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>; <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>
