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

<b>let </b><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  implies  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</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/>



<b>assume </b><a NAME="E1:5"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</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/>

<b>set </b><font color="Maroon" title="c3">C</font> =  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #);<br/>
<a NAME="E2:5"/><i><font color="Green" title="E8">A2</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</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="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <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> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <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> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:5"/><i><font color="Green" title="E9">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</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> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> &amp;  <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 <font color="Maroon" title="c2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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 <font color="Maroon" title="c1">U1</font> )
 
<b>by </b><i><a class="txt" href="pralg_1.html#E1:5"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a>, <a class="ref" href="unialg_2.html#T3" title="UNIALG_2:th.3">UNIALG_2:3</a></i>;<br/>
<a NAME="E4:5"/><i><font color="Green" title="E10">A4</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) is <a href="unialg_1.html#V5" title="UNIALG_1:attr.5">quasi_total</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">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" 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">b<sub>1</sub></font> being  <a href="relset_1.html#M2" title="RELSET_1:mode.2">M5</a>(the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #))  holds <br/>(  not <font color="Maroon" title="c4">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> 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> or <font color="Olive">b<sub>1</sub></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="c5">h</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">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> 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) or  not <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> or <font color="Maroon" title="c5">h</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> )</span><br/>



<b>assume </b><a NAME="E1:5_1"/><i><font color="Green" title="E11">A5</font></i>: 
( <font color="Maroon" title="c4">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> 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) &amp; <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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="c5">h</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">h1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <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 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font> <b>by </b><i><a class="txt" href="pralg_1.html#E2:5"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="pralg_1.html#E3:5"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a>, <a class="ref" href="unialg_1.html#T5" title="UNIALG_1:th.5">UNIALG_1:5</a>, <a class="ref" href="unialg_1.html#D5" title="UNIALG_1:def.5">UNIALG_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">h2</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <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 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font> <b>by </b><i><a class="txt" href="pralg_1.html#E2:5"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="pralg_1.html#E3:5"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="pralg_1.html#E1:5_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a>, <a class="ref" href="unialg_1.html#T5" title="UNIALG_1:th.5">UNIALG_1:5</a>, <a class="ref" href="unialg_1.html#D5" title="UNIALG_1:def.5">UNIALG_1:def 5</a></i>;<br/>
<a NAME="E4:5_1"/>
<font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c6">h1</font>,<font color="Maroon" title="c7">h2</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span>
 
<b>by </b><i><a class="txt" href="pralg_1.html#E1:5"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="pralg_1.html#E1:5_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E5:5_1"/>
<font color="Maroon" title="c5">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>
<a NAME="E5:5"/><i><font color="Green" title="E11">A6</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) is <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">homogeneous</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">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" 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">b<sub>1</sub></font> being  <a href="relset_1.html#M2" title="RELSET_1:mode.2">M5</a>(the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #))  holds <br/>(  not <font color="Maroon" title="c4">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> 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> or <font color="Olive">b<sub>1</sub></font> is <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> )</span><br/><b>let </b><font color="Maroon" title="c5">h</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">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> 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) or  not <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> or <font color="Maroon" title="c5">h</font> is <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> )</span><br/>



<b>assume </b><a NAME="E1:5_2"/><i><font color="Green" title="E12">A7</font></i>: 
( <font color="Maroon" title="c4">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> 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) &amp; <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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="c5">h</font> is <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">h1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <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 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font> <b>by </b><i><a class="txt" href="pralg_1.html#E2:5"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="pralg_1.html#E3:5"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a>, <a class="ref" href="unialg_1.html#T5" title="UNIALG_1:th.5">UNIALG_1:5</a>, <a class="ref" href="unialg_1.html#D5" title="UNIALG_1:def.5">UNIALG_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">h2</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <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 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font> <b>by </b><i><a class="txt" href="pralg_1.html#E2:5"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="pralg_1.html#E3:5"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="pralg_1.html#E1:5_2"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a>, <a class="ref" href="unialg_1.html#T5" title="UNIALG_1:th.5">UNIALG_1:5</a>, <a class="ref" href="unialg_1.html#D5" title="UNIALG_1:def.5">UNIALG_1:def 5</a></i>;<br/>
<a NAME="E4:5_2"/>
<font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c6">h1</font>,<font color="Maroon" title="c7">h2</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span>
 
<b>by </b><i><a class="txt" href="pralg_1.html#E1:5"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="pralg_1.html#E1:5_2"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E5:5_2"/>
<font color="Maroon" title="c5">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>
<a NAME="E6:5"/><i><font color="Green" title="E12">A8</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</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="txt" href="pralg_1.html#E3:5"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a>, <a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/>
<a NAME="E7:5"/>
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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">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="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) or  not 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<b>set </b><font color="Maroon" title="c5">h</font> = 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font>;<br/>
<b>assume </b><a NAME="E1:5_3"/><i><font color="Green" title="E13">A9</font></i>: 
<font color="Maroon" title="c4">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> 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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">m</font> = <font color="Maroon" title="c4">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/>
<b>reconsider </b><font color="Maroon" title="c7">h1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">m</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <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 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font> <b>by </b><i><a class="txt" href="pralg_1.html#E2:5"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="pralg_1.html#E3:5"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="pralg_1.html#E1:5_3"><i><font color="Green" title="E13">A9</font></i></a>, <a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a>, <a class="ref" href="unialg_1.html#T5" title="UNIALG_1:th.5">UNIALG_1:5</a>, <a class="ref" href="unialg_1.html#D5" title="UNIALG_1:def.5">UNIALG_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">h2</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">m</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <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 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font> <b>by </b><i><a class="txt" href="pralg_1.html#E2:5"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="pralg_1.html#E3:5"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="pralg_1.html#E1:5_3"><i><font color="Green" title="E13">A9</font></i></a>, <a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a>, <a class="ref" href="unialg_1.html#T5" title="UNIALG_1:th.5">UNIALG_1:5</a>, <a class="ref" href="unialg_1.html#D5" title="UNIALG_1:def.5">UNIALG_1:def 5</a></i>;<br/>
<a NAME="E5:5_3"/>
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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c8">h2</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span>
 
<b>by </b><i><a class="txt" href="pralg_1.html#E1:5"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="pralg_1.html#E1:5_3"><i><font color="Green" title="E13">A9</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E6:5_3"/>
not 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="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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>hence </b><a NAME="E8:5"/>
 <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</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#E4:5"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="pralg_1.html#E5:5"><i><font color="Green" title="E11">A6</font></i></a>, <a class="txt" href="pralg_1.html#E6:5"><i><font color="Green" title="E12">A8</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
