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<span class="kw">let </span><font color="Maroon" title="c1">Al</font> be    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b2">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font>  st (  for <font color="Olive" title="b3">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span> ) holds <br/> for <font color="Olive" title="b3">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">p</font>)</span>)</span>,<font color="Olive" title="b3">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font>  st (  for <font color="Olive" title="b2">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Olive" title="b2">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span> ) holds <br/> for <font color="Olive" title="b2">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b2">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span> ) implies  for <font color="Olive" title="b1">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span> )</span><br/>





<span class="kw">assume </span><a NAME="E1:34"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
 for <font color="Olive" title="b1">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds   <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">S1</font> = <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">S</font> = <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut2.html#K6" title="SUBSTUT2:func.6">CFQ</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">y</font> =  <a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p1">(<span class="default"><a href="substut1.html#K32" title="SUBSTUT1:func.32">@</a> <span class="p2">(<span class="default"><a href="sublemma.html#K9" title="SUBLEMMA:func.9">CQCSub_All</a> (<span class="p3">(<span class="default"><a href="substut2.html#K7" title="SUBSTUT2:func.7">QScope</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="substut2.html#K8" title="SUBSTUT2:func.8">Qsc</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>)</span>)</span></span>)</span>;<br/>
<a NAME="E2:34"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
 <a href="substut2.html#K7" title="SUBSTUT2:func.7">QScope</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>) is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut2.html#T22" target="_self" onmouseover="rs('substut2/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<span class="lab"><font color="Green" title="E22">A3</font></span>:  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> (<span class="p1">(<span class="default"><a href="substut2.html#K7" title="SUBSTUT2:func.7">QScope</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="substut2.html#K8" title="SUBSTUT2:func.8">Qsc</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>) = 
 <a href="sublemma.html#K9" title="SUBLEMMA:func.9">CQCSub_All</a> (<span class="p1">(<span class="default"><a href="substut2.html#K7" title="SUBSTUT2:func.7">QScope</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="substut2.html#K8" title="SUBSTUT2:func.8">Qsc</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut2.html#T22" target="_self" onmouseover="rs('substut2/T22')" onmouseout="rh()">Th22</a>, <a class="ref" href="sublemma.html#D5" onmouseover="rs('sublemma/D5')" onmouseout="rh()">SUBLEMMA:def 5</a></span>
<br/>.= 
<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut2.html#T22" target="_self" onmouseover="rs('substut2/T22')" onmouseout="rh()">Th22</a></span>
;<br/>
<a NAME="E4:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A4</font></span>: 
<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> 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="#E2:34"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="substut1.html#D28" onmouseover="rs('substut1/D28')" onmouseout="rh()">SUBSTUT1:def 28</a></span>;<br/>
<a NAME="E5:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A5</font></span>: 
 <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCQuant</a> (<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<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#K10" title="SUBLEMMA:func.10">CQCSub_the_scope_of</a> <span class="p3"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sublemma.html#T28" onmouseover="rs('sublemma/T28')" onmouseout="rh()">SUBLEMMA:28</a></span>;<br/>
 <a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_the_scope_of</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> = 
 <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> (<span class="p2">(<span class="default"><a href="substut2.html#K7" title="SUBSTUT2:func.7">QScope</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K8" title="SUBSTUT2:func.8">Qsc</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E4:34"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="sublemma.html#D6" onmouseover="rs('sublemma/D6')" onmouseout="rh()">SUBLEMMA:def 6</a></span>
<br/>.= 
<span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="substut2.html#K6" title="SUBSTUT2:func.6">CFQ</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> <a href="sublemma.html#K8" title="SUBLEMMA:func.8">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="substut1.html#T21" onmouseover="rs('substut1/T21')" onmouseout="rh()">SUBSTUT1:21</a></span>
<br/>.= 
<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut2.html#K6" title="SUBSTUT2:func.6">CFQ</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>

;<br/>
<a NAME="E7:34"/><span class="kw">then </span>
 <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCQuant</a> (<span class="p1">(<span class="default"><a href="sublemma.html#K9" title="SUBLEMMA:func.9">CQCSub_All</a> (<span class="p2">(<span class="default"><a href="substut2.html#K7" title="SUBSTUT2:func.7">QScope</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K8" title="SUBSTUT2:func.8">Qsc</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="substut2.html#K6" title="SUBSTUT2:func.6">CFQ</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="ref" href="substut2.html#T22" target="_self" onmouseover="rs('substut2/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<span class="kw">then </span> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span> = 
 <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3">(<span class="default"><a href="substut1.html#K32" title="SUBSTUT1:func.32">@</a> <span class="p4">(<span class="default"><a href="sublemma.html#K9" title="SUBLEMMA:func.9">CQCSub_All</a> (<span class="p5">(<span class="default"><a href="substut2.html#K7" title="SUBSTUT2:func.7">QScope</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>,<span class="p5">(<span class="default"><a href="substut2.html#K8" title="SUBSTUT2:func.8">Qsc</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">Sub</font>)</span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p3"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut2.html#K6" title="SUBSTUT2:func.6">CFQ</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p5"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut2.html#T22" target="_self" onmouseover="rs('substut2/T22')" onmouseout="rh()">Th22</a>, <a class="ref" href="sublemma.html#T31" onmouseover="rs('sublemma/T31')" onmouseout="rh()">SUBLEMMA:31</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p2">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p3"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut2.html#K6" title="SUBSTUT2:func.6">CFQ</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p5"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_sim1.html#T18" onmouseover="rs('cqc_sim1/T18')" onmouseout="rh()">CQC_SIM1:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E20">A1</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E9:34"/>
 <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_sim1.html#T18" onmouseover="rs('cqc_sim1/T18')" onmouseout="rh()">CQC_SIM1:18</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
