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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a>   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="scmring1.html#NM1" title="SCMRING1:NM.1">SCM-State</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">u</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">u</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="scmring1.html#NM1" title="SCMRING1:NM.1">SCM-State</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">u</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <font color="Maroon" title="c2">s</font>,<font color="Olive" title="b1">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">u</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">u</font></span><br/>





<a NAME="E1:18"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E2:18"/><span class="kw">then </span>
 <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  = 
<span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<font color="Maroon" title="c3">u</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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