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<b>let </b><font color="Maroon">S</font> be    <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">T</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>given </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font><b> such that </b><a NAME="E1:28"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> is <a href="waybel_0.html#V23">isomorphic</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1"/>
( ( not <font color="Maroon">S</font> is <a href="struct_0.html#V3">empty</a> &amp; not <font color="Maroon">T</font> is <a href="struct_0.html#V3">empty</a> ) or <font color="Maroon">S</font> is <a href="struct_0.html#V3">empty</a> or <font color="Maroon">T</font> is <a href="struct_0.html#V3">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1"><b>suppose </b></a><a NAME="E1:28_1_1"/>
( not <font color="Maroon">S</font> is <a href="struct_0.html#V3">empty</a> &amp; not <font color="Maroon">T</font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">s</font> = <font color="Maroon">S</font>, <font color="Maroon">t</font> = <font color="Maroon">T</font> as  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a>  ;<br/><b>given </b><font color="Maroon">X</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><a NAME="E3:28_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">X</font> <a href="lattice3.html#R1">is_&lt;=_than</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4">YELLOW_0:def 4</a><br/><b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">s</font>,<font color="Maroon">t</font> ;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">X</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">s</font> ;<br/><a NAME="E6:28_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font>
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">g</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> ;<br/><b>take </b>
<font color="Maroon">y</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4">YELLOW_0:def 4</a><br/><a NAME="E8:28_1_1"/>
<font color="Maroon">g</font> is <a href="orders_3.html#V5">monotone</a>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/><a NAME="E9:28_1_1"/><b>then </b>
<font color="Maroon">y</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="yellow_2.html#T15">YELLOW_2:15</a></i>;<br/><a NAME="E10:28_1_1"/><b>then </b>
<font color="Maroon">y</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ;<br/><a NAME="E11:28_1_1"/><b>then </b>
<font color="Maroon">y</font> <a href="lattice3.html#R1">is_&lt;=_than</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T45">FUNCT_2:45</a></i>;<br/><b>hence </b><a NAME="E12:28_1_1"/>
<font color="Maroon">y</font> <a href="lattice3.html#R1">is_&lt;=_than</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_2"><b>suppose </b></a><a NAME="E1:28_1_2"/>
( <font color="Maroon">S</font> is <a href="struct_0.html#V3">empty</a> or <font color="Maroon">T</font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/><div class="add"><a NAME="E2:28_1_2"/><b>then </b>
( <font color="Maroon">S</font> is <a href="struct_0.html#V3">empty</a> &amp; <font color="Maroon">T</font> is <a href="struct_0.html#V3">empty</a> )
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/><b>then reconsider </b><font color="Maroon">T</font> = <font color="Maroon">T</font> as  <a href="yellow_0.html#V3">bounded</a>  <a href="orders_2.html#L1">RelStr</a>  <b>by </b><i/>;<br/><a NAME="E4:28_1_2"/>
<font color="Maroon">T</font> is <a href="yellow_0.html#V1">lower-bounded</a>
 ;<br/><b>hence </b><a NAME="E5:28_1_2"/>
(  not <font color="Maroon">S</font> is <a href="yellow_0.html#V1">lower-bounded</a> or <font color="Maroon">T</font> is <a href="yellow_0.html#V1">lower-bounded</a> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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