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<span class="kw">defpred </span><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>] <span class="kw">means </span>$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="E1:92_1_1"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
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>]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#T77" target="_self" title="MIDSP_1:th.77">Th77</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">o</font> being   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of <span class="p1">(<span class="default"><a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:92_1_1"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
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>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S3" title="FUNCT_2:sch.3">FUNCT_2:sch 3</a>(<a class="txt" href="#E1:92_1_1"><span class="lab"><font color="Green" title="E48">A1</font></span></a>);<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c2">o</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">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/>

<span class="kw">thus </span><a NAME="E4:92_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:92_1_1"><span class="lab"><font color="Green" title="E49">A2</font></span></a></span>; <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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