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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A1</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b2">A2</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b1">A1</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> &amp; <font color="Olive" title="b2">A2</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> holds <br/>the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Olive" title="b1">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Olive" title="b2">A2</font></span><br/><b>let </b><font color="Maroon" title="c3">A1</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A2</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Maroon" title="c3">A1</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> &amp; <font color="Olive" title="b1">A2</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> holds <br/>the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Olive" title="b1">A2</font></span><br/><b>let </b><font color="Maroon" title="c4">A2</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">A1</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> &amp; <font color="Maroon" title="c4">A2</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> implies the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font> )</span><br/>





<b>assume </b><a NAME="E1:106"/>
( <font color="Maroon" title="c3">A1</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> &amp; <font color="Maroon" title="c4">A2</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font></span><br/>

<a NAME="E2:106"/><b>then </b>
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  )
 
<b>by </b><i><a class="ref" href="circcomb.html#T65" target="_self" title="CIRCCOMB:th.65">Th65</a></i>;<br/>
<b>hence </b><a NAME="E3:106"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font>
 <b>by </b><i><a class="ref" href="circcomb.html#T4" target="_self" title="CIRCCOMB:th.4">Th4</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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