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<a NAME="E1:31_1"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> <br/>for <font color="Olive">b<sub>2</sub></font> being <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Olive">b<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a> <br/>for <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">F<sub>6</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>) is  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">F<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>)
 
<b>by </b><i><a class="txt" href="circcmb2.html#E1:31"><i><font color="Green">E9</font></i></a></i>;<br/>
<a NAME="E2:31_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">F<sub>2</sub></font>() st ex <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="pboole.html#M1">ManySortedSet</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>8</sub></font>() &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>8</sub></font>() &amp; <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() &amp; ( for <font color="Olive">b<sub>6</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>7</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> <br/>for <font color="Olive">b<sub>8</sub></font> being <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Olive">b<sub>7</sub></font><br/>for <font color="Olive">b<sub>9</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> holds <br/>( <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) &amp; <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) &amp; <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>7</sub></font>(<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) ) ) ) &amp; ex <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="pboole.html#M1">ManySortedSet</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>8</sub></font>() &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>8</sub></font>() &amp; <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() &amp; ( for <font color="Olive">b<sub>6</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>7</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> <br/>for <font color="Olive">b<sub>8</sub></font> being <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Olive">b<sub>7</sub></font><br/>for <font color="Olive">b<sub>9</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> holds <br/>( <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) &amp; <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) &amp; <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>7</sub></font>(<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) ) ) ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 
<b>from </b><i><a class="ref" href="circcmb2.html#S18" target="_self">CIRCCMB2:sch 18</a>(<a class="txt" href="circcmb2.html#E1:31_1"><i><font color="Green">E10</font></i></a>);<br/></i>
<b>hence </b><a NAME="E3:31_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="msualg_1.html#V4">strict</a> <a href="circcomb.html#V4">gate`2=den</a> <a href="circcomb.html#V6">Boolean</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">F<sub>2</sub></font>() st ex <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="pboole.html#M1">ManySortedSet</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>8</sub></font>() &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>8</sub></font>() &amp; <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() &amp; ( for <font color="Olive">b<sub>6</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>7</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> <br/>for <font color="Olive">b<sub>8</sub></font> being <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Olive">b<sub>7</sub></font><br/>for <font color="Olive">b<sub>9</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> holds <br/>( <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) &amp; <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) &amp; <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>7</sub></font>(<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) ) ) ) &amp; ex <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="pboole.html#M1">ManySortedSet</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>8</sub></font>() &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>8</sub></font>() &amp; <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() &amp; ( for <font color="Olive">b<sub>6</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>7</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> <br/>for <font color="Olive">b<sub>8</sub></font> being <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Olive">b<sub>7</sub></font><br/>for <font color="Olive">b<sub>9</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> holds <br/>( <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) &amp; <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) &amp; <font color="Olive">b<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>7</sub></font>(<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>6</sub></font>) ) ) ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/>


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