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

<span class="kw">let </span><font color="Maroon" title="c1">B</font> be   <a href="sublemma.html#V1" title="SUBLEMMA:attr.1">CQC-WFF-like</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">SQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B</font>  st <font color="Maroon" title="c1">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  holds <br/> <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">SQ</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">B</font> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">SQ</font> be    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B</font>; <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">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  implies  <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">B</font> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:46"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c1">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">B</font> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span><br/>

<a NAME="E2:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A2</font></span>: 
 <a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sublemma.html#D6" target="_self" title="SUBLEMMA:def.6">Def6</a></span>;<br/>
<a NAME="E3:46"/><span class="kw">then </span>
 <a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="substut1.html#T14" title="SUBSTUT1:th.14">SUBSTUT1:14</a></span>;<br/>
<a NAME="E4:46"/><span class="kw">then </span>
 <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="sublemma.html#D7" target="_self" title="SUBLEMMA:def.7">Def7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:46"/>
 <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">B</font> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="substut1.html#T21" title="SUBSTUT1:th.21">SUBSTUT1:21</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>
