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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: NOMIN_8:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</font> being   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> <br/>  for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font>, <font color="Olive" title="b4">f3</font>, <font color="Olive" title="b5">f4</font>, <font color="Olive" title="b6">f5</font>, <font color="Olive" title="b7">f6</font>, <font color="Olive" title="b8">f7</font>, <font color="Olive" title="b9">f8</font>, <font color="Olive" title="b10">f9</font> being   <a href="partpr_2.html#NM1" title="PARTPR_2:NM.1">BinominativeFunction</a> of <font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b11">p1</font>, <font color="Olive" title="b12">p2</font>, <font color="Olive" title="b13">p3</font>, <font color="Olive" title="b14">p4</font>, <font color="Olive" title="b15">p5</font>, <font color="Olive" title="b16">p6</font>, <font color="Olive" title="b17">p7</font>, <font color="Olive" title="b18">p8</font>, <font color="Olive" title="b19">p9</font>, <font color="Olive" title="b20">p10</font> being   <a href="partpr_1.html#NM1" title="PARTPR_1:NM.1">PartialPredicate</a> of <font color="Olive" title="b1">D</font>  st <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b11">p1</font>,<font color="Olive" title="b2">f1</font>,<font color="Olive" title="b12">p2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b12">p2</font>,<font color="Olive" title="b3">f2</font>,<font color="Olive" title="b13">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b13">p3</font>,<font color="Olive" title="b4">f3</font>,<font color="Olive" title="b14">p4</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b14">p4</font>,<font color="Olive" title="b5">f4</font>,<font color="Olive" title="b15">p5</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b15">p5</font>,<font color="Olive" title="b6">f5</font>,<font color="Olive" title="b16">p6</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b16">p6</font>,<font color="Olive" title="b7">f6</font>,<font color="Olive" title="b17">p7</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b17">p7</font>,<font color="Olive" title="b8">f7</font>,<font color="Olive" title="b18">p8</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b18">p8</font>,<font color="Olive" title="b9">f8</font>,<font color="Olive" title="b19">p9</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b19">p9</font>,<font color="Olive" title="b10">f9</font>,<font color="Olive" title="b20">p10</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="partpr_2.html#K19" title="PARTPR_2:func.19">PP_inversion</a> <font color="Olive" title="b12">p2</font></span>)</span>,<font color="Olive" title="b3">f2</font>,<font color="Olive" title="b13">p3</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="partpr_2.html#K19" title="PARTPR_2:func.19">PP_inversion</a> <font color="Olive" title="b13">p3</font></span>)</span>,<font color="Olive" title="b4">f3</font>,<font color="Olive" title="b14">p4</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="partpr_2.html#K19" title="PARTPR_2:func.19">PP_inversion</a> <font color="Olive" title="b14">p4</font></span>)</span>,<font color="Olive" title="b5">f4</font>,<font color="Olive" title="b15">p5</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="partpr_2.html#K19" title="PARTPR_2:func.19">PP_inversion</a> <font color="Olive" title="b15">p5</font></span>)</span>,<font color="Olive" title="b6">f5</font>,<font color="Olive" title="b16">p6</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="partpr_2.html#K19" title="PARTPR_2:func.19">PP_inversion</a> <font color="Olive" title="b16">p6</font></span>)</span>,<font color="Olive" title="b7">f6</font>,<font color="Olive" title="b17">p7</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="partpr_2.html#K19" title="PARTPR_2:func.19">PP_inversion</a> <font color="Olive" title="b17">p7</font></span>)</span>,<font color="Olive" title="b8">f7</font>,<font color="Olive" title="b18">p8</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="partpr_2.html#K19" title="PARTPR_2:func.19">PP_inversion</a> <font color="Olive" title="b18">p8</font></span>)</span>,<font color="Olive" title="b9">f8</font>,<font color="Olive" title="b19">p9</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="partpr_2.html#K19" title="PARTPR_2:func.19">PP_inversion</a> <font color="Olive" title="b19">p9</font></span>)</span>,<font color="Olive" title="b10">f9</font>,<font color="Olive" title="b20">p10</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font> holds <br/><span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b11">p1</font>,<span class="p2">(<span class="default"><a href="nomin_8.html#K3" title="NOMIN_8:func.3">PP_composition</a> (<font color="Olive" title="b2">f1</font>,<font color="Olive" title="b3">f2</font>,<font color="Olive" title="b4">f3</font>,<font color="Olive" title="b5">f4</font>,<font color="Olive" title="b6">f5</font>,<font color="Olive" title="b7">f6</font>,<font color="Olive" title="b8">f7</font>,<font color="Olive" title="b9">f8</font>,<font color="Olive" title="b10">f9</font>)</span>)</span>,<font color="Olive" title="b20">p10</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="nomin_3.html#NM2" title="NOMIN_3:NM.2">SFHT</a> of <font color="Olive" title="b1">D</font></div></div>
