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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/> for <font color="Olive" title="b2">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">T</font>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span><br/> for <font color="Olive" title="b3">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">T</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  holds  <font color="Olive" title="b2">f</font> <a href="valued_2.html#K70" title="VALUED_2:func.70">&lt;/&gt;</a> <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="valued_2.html#K91" title="VALUED_2:func.91">&lt;//&gt;</a> <span class="p1">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Olive" title="b3">g</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">T</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span><br/> for <font color="Olive" title="b2">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  holds  <font color="Olive" title="b1">f</font> <a href="valued_2.html#K70" title="VALUED_2:func.70">&lt;/&gt;</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="valued_2.html#K91" title="VALUED_2:func.91">&lt;//&gt;</a> <span class="p1">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Olive" title="b2">g</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  holds  <font color="Maroon" title="c3">f</font> <a href="valued_2.html#K70" title="VALUED_2:func.70">&lt;/&gt;</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="valued_2.html#K91" title="VALUED_2:func.91">&lt;//&gt;</a> <span class="p1">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Olive" title="b1">g</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">f</font> <a href="valued_2.html#K70" title="VALUED_2:func.70">&lt;/&gt;</a> <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="valued_2.html#K91" title="VALUED_2:func.91">&lt;//&gt;</a> <span class="p1">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">I</font> =  <a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">h</font> = <font color="Maroon" title="c3">f</font> <a href="valued_2.html#K70" title="VALUED_2:func.70">&lt;/&gt;</a> <font color="Maroon" title="c4">g</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="toprealc.html#T46" target="_self" title="TOPREALC:th.46">Th46</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">G</font> = <font color="Maroon" title="c3">f</font> <a href="valued_2.html#K91" title="VALUED_2:func.91">&lt;//&gt;</a> <span class="p1">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="toprealc.html#T42" target="_self" title="TOPREALC:th.42">Th42</a></span>;<br/>
<a NAME="E3:91"/>
<font color="Maroon" title="c6">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">G</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">t</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">T</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="funct_2.html#D9" title="FUNCT_2:def.9">FUNCT_2:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">t</font></span><br/>

<a NAME="E1:91_1"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">h</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="c2">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:91_1"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
<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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c8">t</font></span>)</span> <a href="toprealc.html#K9" title="TOPREALC:func.9">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:91_1_1"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</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="c8">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T3" title="EUCLID:th.3">EUCLID:3</a></span>;<br/>
<span class="lab"><font color="Green" title="E40">A4</font></span>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <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="c8">t</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T16" title="VALUED_1:th.16">VALUED_1:16</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:91_1_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:91_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K9" title="TOPREALC:func.9">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T3" title="EUCLID:th.3">EUCLID:3</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="funct_1.html#D17" title="FUNCT_1:def.17">FUNCT_1:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> or <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="toprealc.html#K9" title="TOPREALC:func.9">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> or <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K9" title="TOPREALC:func.9">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E4:91_1_1"/><span class="lab"><font color="Green" title="E41">A5</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K9" title="TOPREALC:func.9">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="toprealc.html#K4" title="TOPREALC:func.4">.</a> <font color="Maroon" title="c9">x</font> = 
<span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K4" title="TOPREALC:func.4">.</a> <font color="Maroon" title="c9">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="toprealc.html#K4" title="TOPREALC:func.4">.</a> <font color="Maroon" title="c9">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T17" title="VALUED_1:th.17">VALUED_1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K4" title="TOPREALC:func.4">.</a> <font color="Maroon" title="c9">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:91_1_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E4:91_1_1"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="ref" href="toprealc.html#T47" target="_self" title="TOPREALC:th.47">Th47</a></span>
<br/>.= 
<span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K4" title="TOPREALC:func.4">.</a> <font color="Maroon" title="c9">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T10" title="VALUED_1:th.10">VALUED_1:10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><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="c8">t</font></span>)</span> <a href="toprealc.html#K9" title="TOPREALC:func.9">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span></span>)</span> <a href="toprealc.html#K4" title="TOPREALC:func.4">.</a> <font color="Maroon" title="c9">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T6" title="VALUED_1:th.6">VALUED_1:6</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:91_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">G</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="c2">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c7">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font> = 
<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="c8">t</font></span>)</span> <a href="toprealc.html#K13" title="TOPREALC:func.13">/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_2.html#D48" title="VALUED_2:def.48">VALUED_2:def 48</a></span>
<br/>.= 
<font color="Maroon" title="c6">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:91_1"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E2:91_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="valued_2.html#D43" title="VALUED_2:def.43">VALUED_2:def 43</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:91"/>
<font color="Maroon" title="c3">f</font> <a href="valued_2.html#K70" title="VALUED_2:func.70">&lt;/&gt;</a> <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="valued_2.html#K91" title="VALUED_2:func.91">&lt;//&gt;</a> <span class="p1">(<span class="default"><a href="toprealc.html#K15" title="TOPREALC:func.15">incl</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">n</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
