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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: NOMIN_8:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font>, <font color="Olive" title="b2">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">loc</font> being  <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b4">d1</font> being    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b5">p</font> being   <a href="nomin_2.html#NM1" title="NOMIN_2:NM.1">SCPartialNominativePredicate</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b6">size</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b7">val</font> being  <font color="Olive">b<sub>6</sub></font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b8">dx</font>, <font color="Olive" title="b9">dy</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b10">NN</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b10">NN</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">size</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 &amp; <font color="Olive" title="b3">loc</font>,<font color="Olive" title="b7">val</font>,<font color="Olive" title="b6">size</font> <a href="nomin_7.html#R3" title="NOMIN_7:pred.3">are_correct_wrt</a> <font color="Olive" title="b4">d1</font> &amp; <font color="Olive" title="b8">dx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="nomin_7.html#K2" title="NOMIN_7:func.2">LocalOverlapSeq</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">loc</font>,<font color="Olive" title="b7">val</font>,<font color="Olive" title="b4">d1</font>,<font color="Olive" title="b6">size</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">size</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> &amp;  <a href="nomin_1.html#K17" title="NOMIN_1:func.17">local_overlapping</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b8">dx</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K18" title="NOMIN_1:func.18">denaming</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<span class="p3">(<span class="default"><font color="Olive" title="b7">val</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">val</font></span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">dx</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">val</font></span>)</span></span>)</span>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b5">p</font> &amp; <font color="Olive" title="b9">dy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K17" title="NOMIN_1:func.17">local_overlapping</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nomin_7.html#K2" title="NOMIN_7:func.2">LocalOverlapSeq</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">loc</font>,<font color="Olive" title="b7">val</font>,<font color="Olive" title="b4">d1</font>,<font color="Olive" title="b6">size</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b10">NN</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K18" title="NOMIN_1:func.18">denaming</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<span class="p3">(<span class="default"><font color="Olive" title="b7">val</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Olive" title="b10">NN</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="nomin_7.html#K2" title="NOMIN_7:func.2">LocalOverlapSeq</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">loc</font>,<font color="Olive" title="b7">val</font>,<font color="Olive" title="b4">d1</font>,<font color="Olive" title="b6">size</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b10">NN</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Olive" title="b10">NN</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>) &amp;  <a href="nomin_1.html#K17" title="NOMIN_1:func.17">local_overlapping</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b9">dy</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K18" title="NOMIN_1:func.18">denaming</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<span class="p3">(<span class="default"><font color="Olive" title="b7">val</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">val</font></span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b9">dy</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">val</font></span>)</span></span>)</span>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b5">p</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nomin_8.html#K8" title="NOMIN_8:func.8">SC_Psuperpos_Seq</a> (<font color="Olive" title="b3">loc</font>,<font color="Olive" title="b7">val</font>,<font color="Olive" title="b5">p</font>)</span>)</span> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nomin_7.html#K2" title="NOMIN_7:func.2">LocalOverlapSeq</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">loc</font>,<font color="Olive" title="b7">val</font>,<font color="Olive" title="b4">d1</font>,<font color="Olive" title="b6">size</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b6">size</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nomin_7.html#K2" title="NOMIN_7:func.2">LocalOverlapSeq</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">loc</font>,<font color="Olive" title="b7">val</font>,<font color="Olive" title="b4">d1</font>,<font color="Olive" title="b6">size</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">size</font></span>)</span></div></div>
