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<span class="kw">set </span><font color="Maroon" title="c2">f</font> =  the    <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>;<br/>
<a NAME="E1:71_1_2"/><span class="lab"><font color="Green" title="E47">A0</font></span>: 
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p2">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D4" title="EQREL_1:def.4">EQREL_1:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">f</font> =  the    <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p2">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">s</font> being   <a href="stacks_1.html#NM2" title="STACKS_1:NM.2">stack</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E4:71_1_2"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
 <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#T2" target="_self" title="STACKS_1:th.2">Th1</a></span>;<br/>
<a NAME="E5:71_1_2"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71_1_2"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="stacks_1.html#T19" target="_self" title="STACKS_1:th.19">Th50</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">E</font> =  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c4">s</font>) as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">g</font> =  the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font>;<br/>
<span class="kw">take </span><font color="Maroon" title="c7">X1</font> =  <a href="stacks_1.html#G1" title="STACKS_1:aggr.1">StackSystem</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p2">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">E</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"> the <a href="stacks_1.html#U2" title="STACKS_1:sel.2">s_push</a> of <font color="Maroon" title="c1">X</font> <a href="stacks_1.html#K3" title="STACKS_1:func.3">/\/</a> <span class="p2">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U3" title="STACKS_1:sel.3">s_pop</a> of <font color="Maroon" title="c1">X</font> <a href="stacks_1.html#K4" title="STACKS_1:func.4">+*</a> <span class="p3">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="filter_1.html#K2" title="FILTER_1:func.2">/\/</a> <span class="p2">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp;  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp;  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  the <a href="stacks_1.html#U2" title="STACKS_1:sel.2">s_push</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="stacks_1.html#U2" title="STACKS_1:sel.2">s_push</a> of <font color="Maroon" title="c1">X</font> <a href="stacks_1.html#K3" title="STACKS_1:func.3">/\/</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp;  the <a href="stacks_1.html#U3" title="STACKS_1:sel.3">s_pop</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U3" title="STACKS_1:sel.3">s_pop</a> of <font color="Maroon" title="c1">X</font> <a href="stacks_1.html#K4" title="STACKS_1:func.4">+*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="filter_1.html#K2" title="FILTER_1:func.2">/\/</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> holds   the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) ) )</span><br/>

<span class="kw">thus </span><a NAME="E7:71_1_2"/>
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp;  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp;  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  the <a href="stacks_1.html#U2" title="STACKS_1:sel.2">s_push</a> of <font color="Maroon" title="c7">X1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  the <a href="stacks_1.html#U2" title="STACKS_1:sel.2">s_push</a> of <font color="Maroon" title="c1">X</font> <a href="stacks_1.html#K3" title="STACKS_1:func.3">/\/</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp;  the <a href="stacks_1.html#U3" title="STACKS_1:sel.3">s_pop</a> of <font color="Maroon" title="c7">X1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U3" title="STACKS_1:sel.3">s_pop</a> of <font color="Maroon" title="c1">X</font> <a href="stacks_1.html#K4" title="STACKS_1:func.4">+*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="filter_1.html#K2" title="FILTER_1:func.2">/\/</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71_1_2"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="stacks_1.html#T19" target="_self" title="STACKS_1:th.19">Th50</a></span>; <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="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> holds   the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">h</font> be    <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">h0</font> = <font color="Maroon" title="c8">h</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p2">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_1_2"><span class="lab"><font color="Green" title="E47">A0</font></span></a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">a</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><span class="kw">consider </span><font color="Maroon" title="c11">s1</font> being   <a href="stacks_1.html#NM2" title="STACKS_1:NM.2">stack</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:71_1_2_1"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c11">s1</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T36" title="EQREL_1:th.36">EQREL_1:36</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:71_1_2_1_1"/>
(  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c11">s1</font> or  not  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c11">s1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:71_1_2_1_1_1"/>
 <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c11">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:71_1_2_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c11">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#D3" target="_self" title="STACKS_1:def.3">EMP</a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E3:71_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A6</font></span>: 
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">E</font> &amp; <font color="Maroon" title="c5">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> &amp; <font color="Maroon" title="c5">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1_2"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E2:71_1_2_1"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="eqrel_1.html#T23" title="EQREL_1:th.23">EQREL_1:23</a></span>;<br/><a NAME="E4:71_1_2_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1_2"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="funct_7.html#T31" title="FUNCT_7:th.31">FUNCT_7:31</a></span>;<br/><span class="kw">hence </span><a NAME="E5:71_1_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1_2"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71_1_2_1_1_1"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="funct_7.html#T31" title="FUNCT_7:th.31">FUNCT_7:31</a></span>; <a class="txt" 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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:71_1_2_1_1_2"/><span class="lab"><font color="Green" title="E51">A4</font></span>: 
 not  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c11">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:71_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">s1</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <font color="Maroon" title="c5">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1_2"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="stacks_1.html#D3" target="_self" title="STACKS_1:def.3">EMP</a></span>;<br/><a NAME="E3:71_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A5</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71_1_2_1"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="eqrel_1.html#T23" title="EQREL_1:th.23">EQREL_1:23</a></span>;<br/><a NAME="E4:71_1_2_1_1_2"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D8" title="SETFAM_1:def.8">SETFAM_1:def 8</a></span>;<br/><a NAME="E5:71_1_2_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">a</font> &amp; <font color="Maroon" title="c8">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_1.html#D1" title="ORDERS_1:def.1">ORDERS_1:def 1</a></span>;<br/><a NAME="E6:71_1_2_1_1_2"/><span class="kw">then </span>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71_1_2_1"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="eqrel_1.html#T18" title="EQREL_1:th.18">EQREL_1:18</a></span>;<br/><a NAME="E7:71_1_2_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c11">s1</font> <a href="stacks_1.html#R2" title="STACKS_1:pred.2">==</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> &amp; <font color="Maroon" title="c11">s1</font> <a href="stacks_1.html#R2" title="STACKS_1:pred.2">==</a> <font color="Maroon" title="c9">h0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#D16" target="_self" title="STACKS_1:def.16">REL</a></span>;<br/><a NAME="E8:71_1_2_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="stacks_1.html#R2" title="STACKS_1:pred.2">==</a> <font color="Maroon" title="c9">h0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> &amp;  not  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_1_2_1_1_2"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="stacks_1.html#T13" target="_self" title="STACKS_1:th.13">Th41</a>, <a class="ref" href="stacks_1.html#T14" target="_self" title="STACKS_1:th.14">Th42</a></span>;<br/><a NAME="E9:71_1_2_1_1_2"/><span class="kw">then </span>
 <a href="stacks_1.html#K6" title="STACKS_1:func.6">top</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="stacks_1.html#K6" title="STACKS_1:func.6">top</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#T18" target="_self" title="STACKS_1:th.18">Th46</a></span>;<br/><a NAME="E10:71_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="stacks_1.html#K6" title="STACKS_1:func.6">top</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>;<br/><a NAME="E11:71_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>;<br/><a NAME="E12:71_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1_2"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71_1_2_1_1_2"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="funct_7.html#T32" title="FUNCT_7:th.32">FUNCT_7:32</a></span>;<br/><span class="kw">hence </span><a NAME="E13:71_1_2_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">h0</font></span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1_2"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71_1_2_1_1_2"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="funct_7.html#T32" title="FUNCT_7:th.32">FUNCT_7:32</a></span>; <a class="txt" 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></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E10:71_1_2"/>
 the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c7">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="stacks_1.html#U4" title="STACKS_1:sel.4">s_top</a> of <font color="Maroon" title="c1">X</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> ( the <a href="stacks_1.html#U1" title="STACKS_1:sel.1">s_empty</a> of <font color="Maroon" title="c1">X</font>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" title="FUNCT_2:th.63">FUNCT_2:63</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
