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<span class="kw">let </span><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  st <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c2">x1</font>,<font color="Olive" title="b1">p</font>) &amp;  ex <font color="Olive" title="b1">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  st <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c3">x2</font>,<font color="Olive" title="b1">p</font>) implies <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c4">p1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> <span class="kw"> such that </span><a NAME="E2:38_1_1"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">p1</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  for <font color="Olive" title="b1">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>   holds  not <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c3">x2</font>,<font color="Olive" title="b1">p</font>) or <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c5">p2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> <span class="kw"> such that </span><a NAME="E4:38_1_1"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">p2</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font></span><br/>

<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">3,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x1</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> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span> = 
 <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">p2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E4:38_1_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="finseq_1.html#T32" title="FINSEQ_1:th.32">FINSEQ_1:32</a></span>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">3,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">x2</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> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T32" title="FINSEQ_1:th.32">FINSEQ_1:32</a></span>
;<br/>
<a NAME="E6:38_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A4</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x1</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> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c4">p1</font></span>)</span> <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="c3">x2</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> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T33" title="FINSEQ_1:th.33">FINSEQ_1:33</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c2">x1</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x1</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> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></span>
<br/>.= 
<font color="Maroon" title="c3">x2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:38_1_1"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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