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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font>,   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font>] <b>means </b>$1 <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K8" title="MIDSP_1:func.8">ID</a> <font color="Maroon" title="c1">M</font>;<br/>
<a NAME="E1:67_1_1"/><i><font color="Green" title="E48">A1</font></i>: 
for <font color="Olive" title="b1">W</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font>  ex <font color="Olive" title="b2">T</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">W</font>,<font color="Olive" title="b2">T</font>]
 
<b>by </b><i><a class="ref" href="midsp_1.html#T77" target="_self" title="MIDSP_1:th.77">Th77</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c2">o</font> being   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font><b> such that </b><br/><a NAME="E3:67_1_1"/><i><font color="Green" title="E49">A2</font></i>: 
for <font color="Olive" title="b1">W</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">W</font>,<font color="Maroon" title="c2">o</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">W</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S3" title="FUNCT_2:sch.3">FUNCT_2:sch 3</a>(<a class="txt" href="midsp_1.html#E1:67_1_1"><i><font color="Green" title="E48">A1</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c2">o</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">W</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font> holds  <font color="Olive" title="b1">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K8" title="MIDSP_1:func.8">ID</a> <font color="Maroon" title="c1">M</font></span><br/>

<b>thus </b><a NAME="E4:67_1_1"/>
for <font color="Olive" title="b1">W</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font> holds  <font color="Olive" title="b1">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K8" title="MIDSP_1:func.8">ID</a> <font color="Maroon" title="c1">M</font>
 <b>by </b><i><a class="txt" href="midsp_1.html#E3:67_1_1"><i><font color="Green" title="E49">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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