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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font> being non <a href="xxreal_0.html#V3">negative</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ex <font color="Olive">b<sub>2</sub></font> being  <a href="alg_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K3" target="_self">dist_toler</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="lang1.html#K17">[*]</a>  &amp;  <a href="eqrel_1.html#K9">Class</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> );<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="partit1.html#K1">PARTITIONS</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:44_1_2"/><i><font color="Green">E36</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> iff ex <font color="Olive">b<sub>2</sub></font> being non <a href="xxreal_0.html#V3">negative</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ex <font color="Olive">b<sub>3</sub></font> being  <a href="alg_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K3" target="_self">dist_toler</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lang1.html#K17">[*]</a>  &amp;  <a href="eqrel_1.html#K9">Class</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) ) ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> iff ex <font color="Olive">b<sub>2</sub></font> being non <a href="xxreal_0.html#V3">negative</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ex <font color="Olive">b<sub>3</sub></font> being  <a href="alg_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K3" target="_self">dist_toler</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lang1.html#K17">[*]</a>  &amp;  <a href="eqrel_1.html#K9">Class</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) ) ) )
 ;<br/>

<a NAME="E2:44_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="partit1.html#K1">PARTITIONS</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> st ( for <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>3</sub></font>] ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>3</sub></font>] ) ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 
<b>from </b><i><a class="ref" href="lmod_7.html#S1">LMOD_7:sch 1</a>();<br/></i>
<b>hence </b><a NAME="E3:44_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="taxonom1.html#E1:44_1_2"><i><font color="Green">E36</font></i></a></i>;<br/>


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