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

<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font><br/> for <font color="Olive" title="b2">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font><br/> for <font color="Olive" title="b3">Sub</font> being  <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> holds  <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">ll</font>,<font color="Olive" title="b3">Sub</font></span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b2">ll</font></span><br/><b>let </b><font color="Maroon" title="c2">P</font> be   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font><br/> for <font color="Olive" title="b2">Sub</font> being  <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> holds  <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">ll</font>,<font color="Olive" title="b2">Sub</font></span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b1">ll</font></span><br/><b>let </b><font color="Maroon" title="c3">ll</font> be   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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> holds  <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Olive" title="b1">Sub</font></span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c3">ll</font></span><br/><b>let </b><font color="Maroon" title="c4">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font></span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c3">ll</font></span><br/>







<a NAME="E1:22"/>
 <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c3">ll</font></span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#T9" title="SUBSTUT1:th.9">SUBSTUT1:9</a></i>;<br/>
<b>hence </b><a NAME="E2:22"/>
<span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font></span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c3">ll</font>
 <b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
