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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>, <font color="Olive" title="b2">g</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> holds  <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K6" title="FINSEQ_8:func.6">ovlrdiff</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K6" title="FINSEQ_8:func.6">ovlrdiff</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span></span><br/>



 <a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>) = 
 <a href="finseq_8.html#K2" title="FINSEQ_8:func.2">smid</a> (<font color="Maroon" title="c3">g</font>,1,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_8.html#D2" onmouseover="rs('finseq_8/D2')" onmouseout="rh()">FINSEQ_8:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c3">g</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_8.html#T5" onmouseover="rs('finseq_8/T5')" onmouseout="rh()">FINSEQ_8:5</a></span>
;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K6" title="FINSEQ_8:func.6">ovlrdiff</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_8.html#D5" onmouseover="rs('finseq_8/D5')" onmouseout="rh()">FINSEQ_8:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c3">g</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#T8" onmouseover="rs('rfinseq/T8')" onmouseout="rh()">RFINSEQ:8</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:32"/>
<font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" title="FINSEQ_8:func.3">ovlpart</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K6" title="FINSEQ_8:func.6">ovlrdiff</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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