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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E3">Def1</font></span>   defines <a href="scmfsa_7.html#K1" title="SCMFSA_7:func.1">:=</a> <a onclick="hs(this)" href="javascript:()">SCMFSA_7:def 1 : <br/></a><span> for <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a><br/>  for <font color="Olive" title="b2">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive">b<sub>3</sub></font> being   <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds <br/> ( ( <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_7.html#K1" title="SCMFSA_7:func.1">:=</a> <font color="Olive" title="b2">k</font> iff  ex <font color="Olive" title="b4">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b4">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">k1</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span> ) ) ) &amp; (  not <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_7.html#K1" title="SCMFSA_7:func.1">:=</a> <font color="Olive" title="b2">k</font> iff  ex <font color="Olive" title="b4">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b4">k1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">k1</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span> ) ) ) );<br/></span></div>
