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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:30_1_1_1"/>
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><a NAME="E2:30_1_1_1"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E3:30_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T9">SCMPDS_4:9</a></i>;<br/><a NAME="E4:30_1_1_1"/><b>then </b><i><font color="Green">E22</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>assume </b><a NAME="E5:30_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><a NAME="E6:30_1_1_1"/><b>then </b>
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E2:30_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="scmpds_3.html#D5">SCMPDS_3:def 5</a></i>;<br/><b>hence </b><a NAME="E7:30_1_1_1"/>
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E4:30_1_1_1"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:30_1_1"/>
 <a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">c<sub>3</sub></font> is <a href="scmpds_3.html#V1">initial</a>
 <b>by </b><i><a class="ref" href="scmpds_3.html#D5">SCMPDS_3:def 5</a></i>;<br/>


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