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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>, <font color="Olive" title="b2">q</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="b3">x</font>, <font color="Olive" title="b4">y</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> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span> &amp; (  <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"><font color="Olive" title="b1">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Olive" title="b2">q</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"><font color="Olive" title="b2">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span> implies  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">q</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"><span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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>, <font color="Olive" title="b2">y</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> holds <br/> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)</span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)</span>)</span> &amp; (  <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"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c3">q</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"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)</span>)</span> implies  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)</span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</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"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> &amp; (  <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"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c3">q</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"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> implies  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> ) )</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</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">S1</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"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">S2</font> = <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>;<br/>
<a NAME="E1:28"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
( <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"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="substut2.html#K5" title="SUBSTUT2:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) &amp; <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="substut2.html#K5" title="SUBSTUT2:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) )
 
;<br/>
<a NAME="E2:28"/>
<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></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#K6" title="SUBLEMMA:func.6">CQCSub_&amp;</a> (<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"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></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#T19" target="_self" onmouseover="rs('substut2/T19')" onmouseout="rh()">Th19</a></span>;<br/>
<a NAME="E3:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> (<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"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="sublemma.html#D3" onmouseover="rs('sublemma/D3')" onmouseout="rh()">SUBLEMMA:def 3</a></span>;<br/>
<a NAME="E4:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<span class="p3">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span></span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</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="c3">q</font>,<span class="p3">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</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="#E1:28"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="substut1.html#T31" onmouseover="rs('substut1/T31')" onmouseout="rh()">SUBSTUT1:31</a></span>;<br/>
<a NAME="E5:28"/>
(  <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"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c3">q</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"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> implies  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="28_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:28_1"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
(  <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"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c3">q</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"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</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">  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span><br/>

<a NAME="E2:28_1"/>
 <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="cqc_sim1.html#T17" onmouseover="rs('cqc_sim1/T17')" onmouseout="rh()">CQC_SIM1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:28_1"/>
 <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="cqc_sim1.html#T17" onmouseover="rs('cqc_sim1/T17')" onmouseout="rh()">CQC_SIM1:17</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:28"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> &amp; (  <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"><font color="Maroon" title="c2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Maroon" title="c3">q</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"><font color="Maroon" title="c3">q</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> implies  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>)</span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="substut1.html#T31" onmouseover="rs('substut1/T31')" onmouseout="rh()">SUBSTUT1:31</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>
