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

<b>let </b><font color="Maroon" title="c2">ll1</font>, <font color="Maroon" title="c3">ll2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-variables</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">k</font> being   <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>  ex <font color="Olive" title="b2">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> ex <font color="Olive" title="b3">ll</font> being   <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Olive" title="b1">k</font> st <br/>( <font color="Maroon" title="c2">ll1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">ll</font> &amp; <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">P</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Olive" title="b3">ll</font> ) &amp;  ex <font color="Olive" title="b1">k</font> being   <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>  ex <font color="Olive" title="b2">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> ex <font color="Olive" title="b3">ll</font> being   <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Olive" title="b1">k</font> st <br/>( <font color="Maroon" title="c3">ll2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">ll</font> &amp; <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">P</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Olive" title="b3">ll</font> ) implies <font color="Maroon" title="c2">ll1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">ll2</font> )</span><br/>

<b>given </b><font color="Maroon" title="c4">k1</font> being    <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> , <font color="Maroon" title="c5">P1</font> being   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c4">k1</font>, <font color="Maroon" title="c6">ll1'</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Maroon" title="c4">k1</font><b> such that </b><a NAME="E2:33_1_2"/><i><font color="Green" title="E25">A3</font></i>: 
( <font color="Maroon" title="c2">ll1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">ll1'</font> &amp; <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P1</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Maroon" title="c6">ll1'</font> )
 ; <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">k</font> being   <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/> for <font color="Olive" title="b2">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font><br/> for <font color="Olive" title="b3">ll</font> being   <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Olive" title="b1">k</font>  holds <br/>(  not <font color="Maroon" title="c3">ll2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">ll</font> or  not <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">P</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Olive" title="b3">ll</font> ) or <font color="Maroon" title="c2">ll1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">ll2</font> )</span><br/>

<b>given </b><font color="Maroon" title="c7">k2</font> being    <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> , <font color="Maroon" title="c8">P2</font> being   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c7">k2</font>, <font color="Maroon" title="c9">ll2'</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Maroon" title="c7">k2</font><b> such that </b><a NAME="E4:33_1_2"/><i><font color="Green" title="E26">A4</font></i>: 
( <font color="Maroon" title="c3">ll2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">ll2'</font> &amp; <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">P2</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Maroon" title="c9">ll2'</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">ll1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">ll2</font></span><br/>

<a NAME="E5:33_1_2"/><i><font color="Green" title="E27">A5</font></i>: 
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">P1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c6">ll1'</font> &amp; <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">P2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c9">ll2'</font> )
 
<b>by </b><i><a class="txt" href="qc_lang1.html#E2:33_1_2"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="qc_lang1.html#E4:33_1_2"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="qc_lang1.html#T23" target="_self" title="QC_LANG1:th.23">Th23</a></i>;<br/>
<font color="Maroon" title="c5">P1</font> = 
 <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <font color="Maroon" title="c1">F</font>
<b>by </b><i><a class="txt" href="qc_lang1.html#E1:33"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="qc_lang1.html#E2:33_1_2"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="qc_lang1.html#D21" target="_self" title="QC_LANG1:def.21">Def21</a></i>
<br/>.= 
<font color="Maroon" title="c8">P2</font>
<b>by </b><i><a class="txt" href="qc_lang1.html#E1:33"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="qc_lang1.html#E4:33_1_2"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="qc_lang1.html#D21" target="_self" title="QC_LANG1:def.21">Def21</a></i>
;<br/>
<b>hence </b><a NAME="E7:33_1_2"/>
<font color="Maroon" title="c2">ll1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">ll2</font>
 <b>by </b><i><a class="txt" href="qc_lang1.html#E2:33_1_2"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="qc_lang1.html#E4:33_1_2"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="qc_lang1.html#E5:33_1_2"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="finseq_1.html#T46" title="FINSEQ_1:th.46">FINSEQ_1:46</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>
