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<a NAME="E1:16_1_1"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
( <font color="Maroon" title="c2">x</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">y</font> is   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> iff <font color="Maroon" title="c2">x</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> (<span class="p1">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Maroon" title="c1">Al</font></span>)</span>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Maroon" title="c1">Al</font></span>)</span>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#D1" onmouseover="rs('substut1/D1')" onmouseout="rh()">SUBSTUT1:def 1</a></span>;<br/>
<a NAME="E2:16_1_1"/>
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T8" onmouseover="rs('funcop_1/T8')" onmouseout="rh()">FUNCOP_1:8</a></span>;<br/>
<a NAME="E3:16_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">y</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Maroon" title="c1">Al</font></span>)</span>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Maroon" title="c1">Al</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T4" onmouseover="rs('relset_1/T4')" onmouseout="rh()">RELSET_1:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:16_1_1"/>
 <a href="substut2.html#NK3" title="SUBSTUT2:NK.3">Sbst</a> (<font color="Maroon" title="c3">y</font>,) is   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="partfun1.html#T45" onmouseover="rs('partfun1/T45')" onmouseout="rh()">PARTFUN1:45</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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