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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#U3" title="MSUALG_1:sel.3">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#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A2</font></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#U3" title="MSUALG_1:sel.3">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#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A2</font></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#U3" title="MSUALG_1:sel.3">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#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A2</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:106"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
<font color="Maroon" title="c3">A1</font> is  <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a> 
 <span class="kw">and </span><br/><a NAME="E2:106"/><span class="lab"><font color="Green" title="E55">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">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#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A2</font></span><br/>

<a NAME="E3:106"/><span class="lab"><font color="Green" title="E56">A3</font></span>: 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">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="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:106"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="circcomb.html#T65" target="_self" title="CIRCCOMB:th.65">Th65</a></span>;<br/>
<a NAME="E4:106"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">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="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="ref" href="circcomb.html#T65" target="_self" title="CIRCCOMB:th.65">Th65</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:106"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">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#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:106"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="ref" href="circcomb.html#T4" target="_self" title="CIRCCOMB:th.4">Th4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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