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<span class="kw">let </span><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font>, <font color="Maroon" title="c3">L3</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>; <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">  for <font color="Olive" title="b1">g1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font><br/>  for <font color="Olive" title="b2">g2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c3">L3</font><br/>  for <font color="Olive" title="b3">d1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font><br/>  for <font color="Olive" title="b4">d2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">L3</font>,<font color="Maroon" title="c2">L2</font>  st <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Olive" title="b1">g1</font>,<font color="Olive" title="b3">d1</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  &amp; <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Olive" title="b2">g2</font>,<font color="Olive" title="b4">d2</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  holds <br/><span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">g1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">d2</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">g1</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font>; <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">  for <font color="Olive" title="b1">g2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c3">L3</font><br/>  for <font color="Olive" title="b2">d1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font><br/>  for <font color="Olive" title="b3">d2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">L3</font>,<font color="Maroon" title="c2">L2</font>  st <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Olive" title="b2">d1</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  &amp; <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Olive" title="b1">g2</font>,<font color="Olive" title="b3">d2</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  holds <br/><span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">d2</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">g2</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c3">L3</font>; <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">  for <font color="Olive" title="b1">d1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font><br/>  for <font color="Olive" title="b2">d2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">L3</font>,<font color="Maroon" title="c2">L2</font>  st <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Olive" title="b1">d1</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  &amp; <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">g2</font>,<font color="Olive" title="b2">d2</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  holds <br/><span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">d2</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">d1</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font>; <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">  for <font color="Olive" title="b1">d2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">L3</font>,<font color="Maroon" title="c2">L2</font>  st <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">d1</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  &amp; <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">g2</font>,<font color="Olive" title="b1">d2</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  holds <br/><span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">d2</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c7">d2</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">L3</font>,<font color="Maroon" title="c2">L2</font>; <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"> ( <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">d1</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  &amp; <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">g2</font>,<font color="Maroon" title="c7">d2</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  implies <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:5"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">d1</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> 
 <span class="kw">and </span><br/><a NAME="E2:5"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">g2</font>,<font color="Maroon" title="c7">d2</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> 
 ; <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"> <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> </span><br/>

<a NAME="E3:5"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
<font color="Maroon" title="c6">d1</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="#E1:5"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="waybel_1.html#T8" onmouseover="rs('waybel_1/T8')" onmouseout="rh()">WAYBEL_1:8</a></span>;<br/>
<a NAME="E4:5"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<font color="Maroon" title="c5">g2</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="#E2:5"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="waybel_1.html#T8" onmouseover="rs('waybel_1/T8')" onmouseout="rh()">WAYBEL_1:8</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E9">A5</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="5_1"><span class="kw">now </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">  for <font color="Olive" title="b1">s</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L3</font><br/>  for <font color="Olive" title="b2">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font> holds <br/> ( ( <font color="Olive" title="b1">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">t</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">t</font> ) &amp; ( <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">t</font> implies <font color="Olive" title="b1">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">t</font> ) )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L3</font>; <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">  for <font color="Olive" title="b1">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font> holds <br/> ( ( <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">t</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b1">t</font> ) &amp; ( <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b1">t</font> implies <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">t</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c9">t</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>; <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"> ( ( <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font> ) &amp; ( <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font> implies <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font> ) )</span><br/><a NAME="E1:5_1"/>
<font color="Maroon" title="c8">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">L3</font>
 ;<br/><a NAME="E2:5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A6</font></span>: 
<font color="Maroon" title="c8">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><a NAME="E3:5_1"/>
<font color="Maroon" title="c9">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>
 ;<br/><a NAME="E4:5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A7</font></span>: 
<font color="Maroon" title="c9">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><span class="kw">thus </span><a NAME="E5:5_1"/>
( <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font> )
  <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"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font> implies <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="5_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_1"/>
<font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font>
 ; <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"> <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font></span><br/>

<a NAME="E2:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:5_1"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>;<br/>
<a NAME="E3:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">d2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="waybel_1.html#T8" onmouseover="rs('waybel_1/T8')" onmouseout="rh()">WAYBEL_1:8</a></span>;<br/>
<a NAME="E4:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">d1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:5"><span class="lab"><font color="Green" title="E7">A3</font></span></a></span>;<br/>
<a NAME="E5:5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A8</font></span>: 
<font color="Maroon" title="c6">d1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:5_1"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>;<br/>
<a NAME="E6:5_1_1"/>
<font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font> <a href="yellow_2.html#R1" title="YELLOW_2:pred.1">&lt;=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">L1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="waybel_1.html#T18" onmouseover="rs('waybel_1/T18')" onmouseout="rh()">WAYBEL_1:18</a></span>;<br/>
<a NAME="E7:5_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">L1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_2.html#T9" onmouseover="rs('yellow_2/T9')" onmouseout="rh()">YELLOW_2:9</a></span>;<br/>
<a NAME="E8:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">d1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">L1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:5_1_1"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/>
<a NAME="E9:5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">d1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E10:5_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</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><span class="kw">end;</span></div><span class="kw">thus </span><a NAME="E6:5_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font> implies <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font> )
  <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><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="5_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font>
 ; <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"> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font></span><br/>

<a NAME="E2:5_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">d1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>;<br/>
<a NAME="E3:5_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">d2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="waybel_1.html#T8" onmouseover="rs('waybel_1/T8')" onmouseout="rh()">WAYBEL_1:8</a></span>;<br/>
<a NAME="E4:5_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:5"><span class="lab"><font color="Green" title="E8">A4</font></span></a></span>;<br/>
<a NAME="E5:5_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>;<br/>
<a NAME="E6:5_1_2"/>
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">L3</font> <a href="yellow_2.html#R1" title="YELLOW_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="waybel_1.html#T18" onmouseover="rs('waybel_1/T18')" onmouseout="rh()">WAYBEL_1:18</a></span>;<br/>
<a NAME="E7:5_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">L3</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_2.html#T9" onmouseover="rs('yellow_2/T9')" onmouseout="rh()">YELLOW_2:9</a></span>;<br/>
<a NAME="E8:5_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">L3</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:5_1_2"><span class="lab"><font color="Green" title="E12">A9</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/>
<a NAME="E9:5_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font></span>)</span>
 
;<br/>
<span class="kw">hence </span><a NAME="E10:5_1_2"/>
<font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:5_1"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</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><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E6:5"/>
<font color="Maroon" title="c7">d2</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="#E2:5"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="waybel_1.html#T8" onmouseover="rs('waybel_1/T8')" onmouseout="rh()">WAYBEL_1:8</a></span>;<br/>
<a NAME="E7:5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A10</font></span>: 
<font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</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="#E3:5"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="ref" href="yellow_2.html#T12" onmouseover="rs('yellow_2/T12')" onmouseout="rh()">YELLOW_2:12</a></span>;<br/>
<a NAME="E8:5"/>
<font color="Maroon" title="c4">g1</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="#E1:5"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="waybel_1.html#T8" onmouseover="rs('waybel_1/T8')" onmouseout="rh()">WAYBEL_1:8</a></span>;<br/>
<a NAME="E9:5"/><span class="kw">then </span>
<font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</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="#E4:5"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="yellow_2.html#T12" onmouseover="rs('yellow_2/T12')" onmouseout="rh()">YELLOW_2:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:5"/>
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">d1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">d2</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:5"><span class="lab"><font color="Green" title="E10">A10</font></span></a>, <a class="txt" href="#E5:5"><span class="lab"><font color="Green" title="E9">A5</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>
