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<b>let </b><font color="Maroon" title="c1">S</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</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">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> implies  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K12" title="SUBLEMMA:func.12">CQCQuant</a> <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c1">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K12" title="SUBLEMMA:func.12">CQCQuant</a> <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:44"/><b>then </b>
 <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="sublemma.html#D7" target="_self" title="SUBLEMMA:def.7">Def7</a></i>;<br/>
<a NAME="E3:44"/><b>then </b>
 <a href="sublemma.html#K12" title="SUBLEMMA:func.12">CQCQuant</a> <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:44"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="sublemma.html#D8" target="_self" title="SUBLEMMA:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E4:44"/>
 <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K12" title="SUBLEMMA:func.12">CQCQuant</a> <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:44"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="substut1.html#T32" title="SUBSTUT1:th.32">SUBSTUT1:32</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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