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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E26">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: NOMIN_7:21</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">z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">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="b5">n0</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  not <font color="Olive" title="b1">V</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Olive" title="b2">A</font> <a href="nomin_4.html#R1" title="NOMIN_4:pred.1">is_without_nonatomicND_wrt</a> <font color="Olive" title="b1">V</font> &amp; (  for <font color="Olive" title="b6">T</font> being    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font> holds <br/> ( <font color="Olive" title="b4">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="nomin_4.html#R4" title="NOMIN_4:pred.4">is_a_value_on</a> <font color="Olive" title="b6">T</font> &amp; <font color="Olive" title="b4">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3 <a href="nomin_4.html#R4" title="NOMIN_4:pred.4">is_a_value_on</a> <font color="Olive" title="b6">T</font> ) ) holds <br/><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_1.html#K6" title="PARTPR_1:func.6">PP_and</a> (<span class="p3">(<span class="default"><a href="nomin_4.html#K5" title="NOMIN_4:func.5">Equality</a> (<font color="Olive" title="b2">A</font>,<span class="p4">(<span class="default"><font color="Olive" title="b4">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Olive" title="b4">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span>)</span>)</span>,<span class="p3">(<span class="default"><a href="nomin_7.html#K11" title="NOMIN_7:func.11">Fibonacci_inv</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b4">loc</font>,<font color="Olive" title="b5">n0</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="nomin_2.html#K6" title="NOMIN_2:func.6">SC_assignment</a> (<span class="p3">(<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="p4">(<span class="default"><font color="Olive" title="b4">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 4</span>)</span>)</span>)</span>,<font color="Olive" title="b3">z</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="nomin_7.html#K10" title="NOMIN_7:func.10">valid_Fibonacci_output</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b5">n0</font>)</span>)</span></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 <span class="p1">(<span class="default"><a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>)</span>)</span></div></div>
