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<b>let </b><font color="Maroon" title="c1">DK</font>, <font color="Maroon" title="c2">DX</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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"> for <font color="Olive" title="b1">f</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">DK</font>  st <font color="Olive" title="b1">f</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Olive" title="b1">f</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Olive" title="b1">f</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  holds <br/>for <font color="Olive" title="b2">Y1</font>, <font color="Olive" title="b3">Y2</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b2">Y1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">Y2</font> holds <br/>for <font color="Olive" title="b4">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>  st <font color="Olive" title="b2">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b4">F</font> &amp; <font color="Olive" title="b3">Y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b4">F</font> holds <br/>for <font color="Olive" title="b5">Z</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b5">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">Y2</font> holds <br/> <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b5">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b4">F</font>,<font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b2">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b4">F</font>,<font color="Olive" title="b1">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b3">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b4">F</font>,<font color="Olive" title="b1">f</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">DK</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon" title="c3">f</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Maroon" title="c3">f</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  implies for <font color="Olive" title="b1">Y1</font>, <font color="Olive" title="b2">Y2</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b1">Y1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">Y2</font> holds <br/>for <font color="Olive" title="b3">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>  st <font color="Olive" title="b1">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">F</font> &amp; <font color="Olive" title="b2">Y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">F</font> holds <br/>for <font color="Olive" title="b4">Z</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b4">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">Y2</font> holds <br/> <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b4">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b3">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b1">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b3">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b2">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b3">F</font>,<font color="Maroon" title="c3">f</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green" title="E13">A1</font></i>: 
( <font color="Maroon" title="c3">f</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon" title="c3">f</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Maroon" title="c3">f</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</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">Y1</font>, <font color="Olive" title="b2">Y2</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b1">Y1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">Y2</font> holds <br/>for <font color="Olive" title="b3">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>  st <font color="Olive" title="b1">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">F</font> &amp; <font color="Olive" title="b2">Y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">F</font> holds <br/>for <font color="Olive" title="b4">Z</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b4">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">Y2</font> holds <br/> <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b4">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b3">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b1">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b3">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b2">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b3">F</font>,<font color="Maroon" title="c3">f</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c4">Y1</font>, <font color="Maroon" title="c5">Y2</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">Y1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">Y2</font> implies for <font color="Olive" title="b1">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>  st <font color="Maroon" title="c4">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">F</font> &amp; <font color="Maroon" title="c5">Y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">F</font> holds <br/>for <font color="Olive" title="b2">Z</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">Y2</font> holds <br/> <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b2">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c3">f</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E2:25"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c4">Y1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">Y2</font>
 ; <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">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>  st <font color="Maroon" title="c4">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">F</font> &amp; <font color="Maroon" title="c5">Y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">F</font> holds <br/>for <font color="Olive" title="b2">Z</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">Y2</font> holds <br/> <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b2">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Olive" title="b1">F</font>,<font color="Maroon" title="c3">f</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c6">F</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">F</font> &amp; <font color="Maroon" title="c5">Y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">F</font> implies for <font color="Olive" title="b1">Z</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b1">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">Y2</font> holds <br/> <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b1">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E3:25"/><i><font color="Green" title="E15">A3</font></i>: 
( <font color="Maroon" title="c4">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">F</font> &amp; <font color="Maroon" title="c5">Y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">F</font> )
 ; <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">Z</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>  st <font color="Olive" title="b1">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">Y2</font> holds <br/> <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Olive" title="b1">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c7">Z</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">DX</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">Y2</font> implies  <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c7">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E4:25"/><i><font color="Green" title="E16">A4</font></i>: 
<font color="Maroon" title="c7">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">Y2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c7">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span></span><br/>

<a NAME="E5:25"/><b>then </b><i><font color="Green" title="E17">A5</font></i>: 
<font color="Maroon" title="c7">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">F</font>
 
<b>by </b><i><a class="txt" href="bhsp_5.html#E3:25"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">p1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c2">DX</font><b> such that </b><br/><a NAME="E7:25"/><i><font color="Green" title="E18">A6</font></i>: 
<font color="Maroon" title="c8">p1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E8:25"/><i><font color="Green" title="E19">A7</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c8">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y1</font>
 <b>and </b><br/><a NAME="E9:25"/><i><font color="Green" title="E20">A8</font></i>: 
 <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K4" title="BHSP_5:func.4">Func_Seq</a> <font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c8">p1</font></span>)</span>
 <b>by </b><i><a class="txt" href="bhsp_5.html#E1:25"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="bhsp_5.html#E3:25"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="bhsp_5.html#D5" target="_self" title="BHSP_5:def.5">Def5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">p2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c2">DX</font><b> such that </b><br/><a NAME="E11:25"/><i><font color="Green" title="E21">A9</font></i>: 
<font color="Maroon" title="c9">p2</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E12:25"/><i><font color="Green" title="E22">A10</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c9">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Y2</font>
 <b>and </b><br/><a NAME="E13:25"/><i><font color="Green" title="E23">A11</font></i>: 
 <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K4" title="BHSP_5:func.4">Func_Seq</a> <font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c9">p2</font></span>)</span>
 <b>by </b><i><a class="txt" href="bhsp_5.html#E1:25"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="bhsp_5.html#E3:25"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="bhsp_5.html#D5" target="_self" title="BHSP_5:def.5">Def5</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">q</font> = <font color="Maroon" title="c8">p1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c9">p2</font>;<br/>
<a NAME="E14:25"/><i><font color="Green" title="E24">A12</font></i>: 
<font color="Maroon" title="c8">p1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c9">p2</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="bhsp_5.html#E2:25"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="bhsp_5.html#E7:25"><i><font color="Green" title="E18">A6</font></i></a>, <a class="txt" href="bhsp_5.html#E8:25"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="bhsp_5.html#E11:25"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="bhsp_5.html#E12:25"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="finseq_3.html#T98" title="FINSEQ_3:th.98">FINSEQ_3:98</a></i>;<br/>
<a NAME="E15:25"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">p1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c9">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Z</font>
 
<b>by </b><i><a class="txt" href="bhsp_5.html#E4:25"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="bhsp_5.html#E8:25"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="bhsp_5.html#E12:25"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>;<br/>
<a NAME="E16:25"/><b>then </b><i><font color="Green" title="E25">A13</font></i>: 
 <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c7">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K4" title="BHSP_5:func.4">Func_Seq</a> <font color="Maroon" title="c6">F</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">p1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c9">p2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bhsp_5.html#E1:25"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="bhsp_5.html#E5:25"><i><font color="Green" title="E17">A5</font></i></a>, <a class="txt" href="bhsp_5.html#E14:25"><i><font color="Green" title="E24">A12</font></i></a>, <a class="ref" href="bhsp_5.html#D5" target="_self" title="BHSP_5:def.5">Def5</a></i>;<br/>
<a NAME="E17:25"/><i><font color="Green" title="E26">A14</font></i>: 
 ex <font color="Olive" title="b1">fp1</font>, <font color="Olive" title="b2">fp2</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <br/>( <font color="Olive" title="b1">fp1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c8">p1</font> &amp; <font color="Olive" title="b2">fp2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c9">p2</font> &amp; <font color="Maroon" title="c6">F</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">p1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c9">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">fp1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">fp2</font> )
 
<b>by </b><i><a class="txt" href="bhsp_5.html#E4:25"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="bhsp_5.html#E3:25"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a>, <a class="txt" href="bhsp_5.html#E8:25"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="bhsp_5.html#E12:25"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="hilbasis.html#T1" title="HILBASIS:th.1">HILBASIS:1</a></i>;<br/>
<b>thus </b><a NAME="E18:25"/>
 <a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c7">Z</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="bhsp_5.html#K5" title="BHSP_5:func.5">setopfunc</a> <font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c2">DX</font>,<font color="Maroon" title="c1">DK</font>,<font color="Maroon" title="c6">F</font>,<font color="Maroon" title="c3">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="bhsp_5.html#E1:25"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="bhsp_5.html#E9:25"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="bhsp_5.html#E13:25"><i><font color="Green" title="E23">A11</font></i></a>, <a class="txt" href="bhsp_5.html#E16:25"><i><font color="Green" title="E25">A13</font></i></a>, <a class="txt" href="bhsp_5.html#E17:25"><i><font color="Green" title="E26">A14</font></i></a>, <a class="ref" href="finsop_1.html#T6" title="FINSOP_1:th.6">FINSOP_1:6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
