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<b>let </b><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">f1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">f2</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f1</font> holds <br/><font color="Maroon" title="c1">f1</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Olive" title="b1">p</font></span><br/><b>let </b><font color="Maroon" title="c3">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">f1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">f2</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f1</font> implies <font color="Maroon" title="c1">f1</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Maroon" title="c3">p</font> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:21"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c1">f1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">f2</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Maroon" title="c3">p</font>
 <b>and </b><br/><a NAME="E2:21"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">f1</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Maroon" title="c3">p</font></span><br/>

<a NAME="E3:21"/><i><font color="Green" title="E20">A3</font></i>: 
not <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">|--</a> <font color="Maroon" title="c3">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_6.html#E1:21"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="finseq_4.html#T60" title="FINSEQ_4:th.60">FINSEQ_4:60</a></i>;<br/>
<a NAME="E4:21"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">|--</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">|--</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">f2</font>
 
<b>by </b><i><a class="txt" href="finseq_6.html#E2:21"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="finseq_6.html#T10" target="_self" title="FINSEQ_6:th.10">Th10</a></i>;<br/>
<a NAME="E5:21"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">|--</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">|--</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>;<br/>
<a NAME="E6:21"/><b>then </b>
not <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">|--</a> <font color="Maroon" title="c3">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_6.html#E3:21"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:21"/>
<font color="Maroon" title="c1">f1</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Maroon" title="c3">p</font>
 <b>by </b><i><a class="txt" href="finseq_6.html#E2:21"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="finseq_4.html#T60" title="FINSEQ_4:th.60">FINSEQ_4:60</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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