<?xml version="1.0"?>
<div class="add">

<a NAME="E1:35_1_1"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">k</font> being    <a href="orders_3.html#M1" title="ORDERS_3:mode.1">Element</a> of <font color="Maroon" title="c1">P</font><br/>  for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="orders_3.html#K1" title="ORDERS_3:func.1">MonFuncs</a> (<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>) &amp; <font color="Olive" title="b5">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="orders_3.html#K1" title="ORDERS_3:func.1">MonFuncs</a> (<font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font>) holds <br/><font color="Olive" title="b5">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b4">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="orders_3.html#K1" title="ORDERS_3:func.1">MonFuncs</a> (<font color="Olive" title="b1">i</font>,<font color="Olive" title="b3">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_3.html#T6" target="_self" onmouseover="rs('orders_3/T6')" onmouseout="rh()">Th6</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:35_1_1"/>
 ex <font color="Olive" title="b1">C</font> being   <a href="altcat_1.html#V6" title="ALTCAT_1:attr.6">strict</a>   <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a>  st <br/>(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P</font> &amp; (  for <font color="Olive" title="b2">i</font>, <font color="Olive" title="b3">j</font> being    <a href="orders_3.html#M1" title="ORDERS_3:mode.1">Element</a> of <font color="Maroon" title="c1">P</font> holds <br/> (  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Olive" title="b1">C</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">i</font>,<font color="Olive" title="b3">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_3.html#K1" title="ORDERS_3:func.1">MonFuncs</a> (<font color="Olive" title="b2">i</font>,<font color="Olive" title="b3">j</font>) &amp; (  for <font color="Olive" title="b4">i</font>, <font color="Olive" title="b5">j</font>, <font color="Olive" title="b6">k</font> being    <a href="orders_3.html#M1" title="ORDERS_3:mode.1">Element</a> of <font color="Maroon" title="c1">P</font> holds   the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Olive" title="b1">C</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> (<font color="Olive" title="b4">i</font>,<font color="Olive" title="b5">j</font>,<font color="Olive" title="b6">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K6" title="ALTCAT_1:func.6">FuncComp</a> (<span class="p1">(<span class="default"><a href="orders_3.html#K1" title="ORDERS_3:func.1">MonFuncs</a> (<font color="Olive" title="b4">i</font>,<font color="Olive" title="b5">j</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="orders_3.html#K1" title="ORDERS_3:func.1">MonFuncs</a> (<font color="Olive" title="b5">j</font>,<font color="Olive" title="b6">k</font>)</span>)</span>) ) ) ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="orders_3.html#S1" target="_self" onmouseover="rs('orders_3/S1')" onmouseout="rh()">ORDERS_3:sch 1</a>(<a class="txt" href="#E1:35_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>);</span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
