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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">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">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><br/>  for <font color="Olive" title="b4">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font>,<font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b5">l</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font>,<font color="Maroon" title="c1">Al</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b5">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Olive" title="b5">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>)</span>)</span>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b5">l</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="b4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b5">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>)</span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">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><br/>  for <font color="Olive" title="b3">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b4">l</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c1">Al</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b4">l</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> <font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Olive" title="b4">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)</span>)</span>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b4">l</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="b3">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b4">l</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="c3">x</font>, <font color="Maroon" title="c4">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">  for <font color="Olive" title="b1">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b2">l</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c2">k</font>,<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#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b2">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Olive" title="b2">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>)</span>)</span> &amp;  <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#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b2">l</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#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b2">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">P</font> be   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Maroon" title="c2">k</font>,<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">l</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c1">Al</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b1">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Olive" title="b1">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b1">l</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="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b1">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">l</font> be   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c2">k</font>,<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="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Maroon" title="c6">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</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="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> )</span><br/>











<span class="kw">set </span><font color="Maroon" title="c7">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="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>;<br/>
<a NAME="E1:21"/>
<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="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">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#K4" title="SUBLEMMA:func.4">Sub_P</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">l</font>,<span class="p1">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T9" onmouseover="rs('substut1/T9')" onmouseout="rh()">SUBSTUT1:9</a></span>;<br/>
<a NAME="E2:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Maroon" title="c6">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sublemma.html#T8" onmouseover="rs('sublemma/T8')" onmouseout="rh()">SUBLEMMA:8</a></span>;<br/>
<a NAME="E3:21"/>
 <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p2">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Maroon" title="c6">l</font>,<span class="p3">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_sim1.html#T15" onmouseover="rs('cqc_sim1/T15')" onmouseout="rh()">CQC_SIM1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:21"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> (<font color="Maroon" title="c6">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>)</span>)</span> &amp;  <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</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="c5">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="cqc_sim1.html#T15" onmouseover="rs('cqc_sim1/T15')" onmouseout="rh()">CQC_SIM1:15</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/>


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