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<span class="kw">let </span><font color="Maroon" title="c2">F1</font>, <font color="Maroon" title="c3">F2</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </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">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> holds <br/> ( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F1</font> iff  ex <font color="Olive" title="b2">s</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">S</font> st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Olive" title="b2">s</font> ) ) &amp; ( for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> holds <br/> ( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F2</font> iff  ex <font color="Olive" title="b2">s</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">S</font> st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Olive" title="b2">s</font> ) ) implies <font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17_1_2"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> holds <br/> ( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">A</font>] )
 <span class="kw">and </span><br/><a NAME="E2:17_1_2"/><span class="lab"><font color="Green" title="E10">A3</font></span>: 
for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> holds <br/> ( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">A</font>] )
 ; <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="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font></span><br/>

<span class="kw">thus </span><a NAME="E3:17_1_2"/>
<font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font>
 <span class="kw">from</span> <span class="lab"><a class="ref" href="subset_1.html#S4" title="SUBSET_1:sch.4">SUBSET_1:sch 4</a>(<a class="txt" href="#E1:17_1_2"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E2:17_1_2"><span class="lab"><font color="Green" title="E10">A3</font></span></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/>


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