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<span class="kw">let </span><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>  st  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T</font> #) &amp; <font color="Olive" title="b1">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">g</font> &amp; <font color="Olive" title="b1">f</font> is  <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a>  holds <br/><font color="Olive" title="b2">g</font> is  <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>  st  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T</font> #) &amp; <font color="Maroon" title="c3">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">g</font> &amp; <font color="Maroon" title="c3">f</font> is  <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a>  holds <br/><font color="Olive" title="b1">g</font> is  <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T</font> #) &amp; <font color="Maroon" title="c3">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c4">g</font> &amp; <font color="Maroon" title="c3">f</font> is  <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a>  implies <font color="Maroon" title="c4">g</font> is  <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a>  )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T</font> #)
 <span class="kw">and </span><br/><a NAME="E2:36"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c4">g</font>
 <span class="kw">and </span><br/><a NAME="E3:36"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
( <font color="Maroon" title="c3">f</font> is  <a href="quantal1.html#V11" title="QUANTAL1:attr.11">idempotent</a>  &amp; <font color="Maroon" title="c3">f</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  )
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_1.html#D13" title="WAYBEL_1:def.13">WAYBEL_1:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">g</font> is  <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a> </span><br/>

<span class="kw">thus </span><a NAME="E4:36"/>
( <font color="Maroon" title="c4">g</font> is  <a href="quantal1.html#V11" title="QUANTAL1:attr.11">idempotent</a>  &amp; <font color="Maroon" title="c4">g</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="waybel_9.html#T1" title="WAYBEL_9:th.1">WAYBEL_9:1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_1.html#D13" title="WAYBEL_1:def.13">WAYBEL_1:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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