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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>,  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c2">SCS</font>) <b>-&gt; </b>  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c2">SCS</font> =  <a href="circuit2.html#K7" title="CIRCUIT2:func.7">Following</a> $2,<span class="p1">(<span class="default"><span class="p2">(<span class="default">$1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="circuit1.html#K2" title="CIRCUIT1:func.2">-th_InputValues</a> <font color="Maroon" title="c3">InpFs</font></span>)</span>;<br/>
<b>thus </b><a NAME="E1:22_1_1"/>
(  ex <font color="Olive" title="b1">IT</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">SCS</font> st <br/>( <font color="Olive" title="b1">IT</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit2.html#K8" title="CIRCUIT2:func.8">InitialComp</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">InpFs</font> &amp; ( for <font color="Olive" title="b2">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Olive" title="b1">IT</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">i</font>,<font color="Olive" title="b1">IT</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">i</font>) ) ) &amp; ( for <font color="Olive" title="b1">IT1</font>, <font color="Olive" title="b2">IT2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">SCS</font>  st <font color="Olive" title="b1">IT1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit2.html#K8" title="CIRCUIT2:func.8">InitialComp</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">InpFs</font> &amp; ( for <font color="Olive" title="b3">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Olive" title="b1">IT1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">i</font>,<font color="Olive" title="b1">IT1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">i</font>) ) &amp; <font color="Olive" title="b2">IT2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit2.html#K8" title="CIRCUIT2:func.8">InitialComp</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">InpFs</font> &amp; ( for <font color="Olive" title="b3">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Olive" title="b2">IT2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">i</font>,<font color="Olive" title="b2">IT2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">i</font>) ) holds <br/><font color="Olive" title="b1">IT1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">IT2</font> ) )
 <b>from </b><i><a class="ref" href="pre_circ.html#S3" title="PRE_CIRC:sch.3">PRE_CIRC:sch 3</a>();</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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