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<a NAME="E1:150_1_1"/><span class="lab"><font color="Green" title="E67">A</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:150_1_1"/><span class="lab"><font color="Green" title="E68">B0</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S9" title="FUNCT_2:sch.9">FUNCT_2:sch 9</a>(<a class="txt" href="#E1:150_1_1"><span class="lab"><font color="Green" title="E67">A</font></span></a>);<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c5">f</font>
; <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">q</font> being  <font color="Maroon" title="c1">U</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds  <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">u</font>) <a href="fomodel0.html#K19" title="FOMODEL0:func.19">-SymbolSubstIn</a> <font color="Olive" title="b1">q</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="150_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">q</font> be  <font color="Maroon" title="c1">U</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">u</font>) <a href="fomodel0.html#K19" title="FOMODEL0:func.19">-SymbolSubstIn</a> <font color="Maroon" title="c6">q</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c7">qq</font> = <font color="Maroon" title="c6">q</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">U</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel0.html#E5"><span class="lab"><font color="Green" title="E4">Lm45</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">qqq</font> = <font color="Maroon" title="c7">qq</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/><a NAME="E3:150_1_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">qqq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c8">qqq</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:150_1_1"><span class="lab"><font color="Green" title="E68">B0</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:150_1_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">u</font>) <a href="fomodel0.html#K19" title="FOMODEL0:func.19">-SymbolSubstIn</a> <font color="Maroon" title="c6">q</font>
 ; <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>
<span class="kw">hence </span><a NAME="E5:150_1_1"/>
 for <font color="Olive" title="b1">q</font> being  <font color="Maroon" title="c1">U</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds  <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">u</font>) <a href="fomodel0.html#K19" title="FOMODEL0:func.19">-SymbolSubstIn</a> <font color="Olive" title="b1">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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