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<span class="kw">let </span><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">S9</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</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>, <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="c1">S</font>  st the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A1</font> <a href="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A2</font> holds <br/>for <font color="Olive" title="b3">h</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b1">A1</font>,<font color="Olive" title="b2">A2</font>  st <font color="Olive" title="b3">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b1">A1</font>,<font color="Olive" title="b2">A2</font> holds <br/>for <font color="Olive" title="b4">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S9</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b5">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">f</font>,<font color="Olive" title="b5">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c1">S</font> holds <br/> ex <font color="Olive" title="b6">h9</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b5">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b5">g</font></span>)</span> st <br/>( <font color="Olive" title="b6">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b4">f</font> &amp; <font color="Olive" title="b6">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b1">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b5">g</font>,<font color="Olive" title="b2">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b5">g</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A1</font>, <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="c1">S</font>; <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="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A2</font> implies for <font color="Olive" title="b1">h</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">A1</font>,<font color="Maroon" title="c4">A2</font>  st <font color="Olive" title="b1">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font>,<font color="Maroon" title="c4">A2</font> holds <br/>for <font color="Olive" title="b2">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S9</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b3">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c1">S</font> holds <br/> ex <font color="Olive" title="b4">h9</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font></span>)</span> st <br/>( <font color="Olive" title="b4">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b2">f</font> &amp; <font color="Olive" title="b4">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:44"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A2</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">h</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">A1</font>,<font color="Maroon" title="c4">A2</font>  st <font color="Olive" title="b1">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font>,<font color="Maroon" title="c4">A2</font> holds <br/>for <font color="Olive" title="b2">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S9</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b3">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c1">S</font> holds <br/> ex <font color="Olive" title="b4">h9</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font></span>)</span> st <br/>( <font color="Olive" title="b4">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b2">f</font> &amp; <font color="Olive" title="b4">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">h</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">A1</font>,<font color="Maroon" title="c4">A2</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="c5">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font>,<font color="Maroon" title="c4">A2</font> implies for <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S9</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c1">S</font> holds <br/> ex <font color="Olive" title="b3">h9</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span> st <br/>( <font color="Olive" title="b3">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b3">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:44"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c5">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font>,<font color="Maroon" title="c4">A2</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">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S9</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c1">S</font> holds <br/> ex <font color="Olive" title="b3">h9</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span> st <br/>( <font color="Olive" title="b3">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b3">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S9</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</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">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon" title="c6">f</font>,<font color="Olive" title="b1">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c1">S</font> holds <br/> ex <font color="Olive" title="b2">h9</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Olive" title="b1">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Olive" title="b1">g</font></span>)</span> st <br/>( <font color="Olive" title="b2">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">f</font> &amp; <font color="Olive" title="b2">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Olive" title="b1">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Olive" title="b1">g</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <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="c6">f</font>,<font color="Maroon" title="c7">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c1">S</font> implies  ex <font color="Olive" title="b1">h9</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> st <br/>( <font color="Olive" title="b1">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">f</font> &amp; <font color="Olive" title="b1">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E3:44"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">h9</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> st <br/>( <font color="Olive" title="b1">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">f</font> &amp; <font color="Olive" title="b1">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font> )</span><br/>

<a NAME="E4:44"/><span class="lab"><font color="Green" title="E28">A4</font></span>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S9</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="pua2mss1.html#D13" title="PUA2MSS1:def.13">PUA2MSS1:def 13</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">B1</font> = <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">B2</font> = <font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">g</font> = <font color="Maroon" title="c7">g</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S9</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></span>;<br/>
<a NAME="E6:44"/><span class="lab"><font color="Green" title="E29">A5</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c10">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="pua2mss1.html#D13" title="PUA2MSS1:def.13">PUA2MSS1:def 13</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">h9</font> = <font color="Maroon" title="c5">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">f</font> as   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="instalg1.html#T30" target="_self" title="INSTALG1:th.30">Th30</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c11">h9</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="c11">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">f</font> &amp; <font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font> )</span><br/>

<span class="kw">thus </span><a NAME="E8:44"/>
<font color="Maroon" title="c11">h9</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">f</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="c11">h9</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c12">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S9</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="msualg_3.html#D9" title="MSUALG_3:def.9">MSUALG_3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c12">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c13">go</font> = <font color="Maroon" title="c10">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">o</font>;<br/>
<span class="kw">assume </span><a NAME="E9:44"/><span class="lab"><font color="Green" title="E30">A6</font></span>: 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c12">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c14">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c12">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c14">x</font></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c15">y</font> = <font color="Maroon" title="c14">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">o</font></span>)</span>,<font color="Maroon" title="c3">A1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="instalg1.html#T25" target="_self" title="INSTALG1:th.25">Th25</a></span>;<br/>
<span class="lab"><font color="Green" title="E31">A7</font></span>: <font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c12">o</font></span>)</span> = 
<font color="Maroon" title="c5">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c12">o</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
<br/>.= 
<font color="Maroon" title="c5">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c10">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">o</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:44"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
<br/>.= 
<font color="Maroon" title="c5">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">o</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
;<br/>
<a NAME="E12:44"/><span class="lab"><font color="Green" title="E32">A8</font></span>: 
(  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">o</font></span>)</span>,<font color="Maroon" title="c3">A1</font> &amp;  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">o</font></span>)</span>,<font color="Maroon" title="c4">A2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="instalg1.html#T24" target="_self" title="INSTALG1:th.24">Th24</a></span>;<br/>
<a NAME="E13:44"/><span class="lab"><font color="Green" title="E33">A9</font></span>: 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">o</font></span>)</span>,<font color="Maroon" title="c3">A1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="instalg1.html#T25" target="_self" title="INSTALG1:th.25">Th25</a></span>;<br/>
<a NAME="E14:44"/><span class="lab"><font color="Green" title="E34">A10</font></span>: 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">o</font></span>)</span>,<font color="Maroon" title="c4">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="instalg1.html#T25" target="_self" title="INSTALG1:th.25">Th25</a></span>;<br/>
<a NAME="E15:44"/><span class="kw">then </span>
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">o</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E9:44"><span class="lab"><font color="Green" title="E30">A6</font></span></a>, <a class="txt" href="#E13:44"><span class="lab"><font color="Green" title="E33">A9</font></span></a>, <a class="ref" href="instalg1.html#T3" target="_self" title="INSTALG1:th.3">Th3</a></span>;<br/>
<a NAME="E16:44"/><span class="kw">then </span>
<font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c15">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="txt" href="#E9:44"><span class="lab"><font color="Green" title="E30">A6</font></span></a>, <a class="txt" href="#E13:44"><span class="lab"><font color="Green" title="E33">A9</font></span></a>, <a class="txt" href="#E14:44"><span class="lab"><font color="Green" title="E34">A10</font></span></a>, <a class="ref" href="instalg1.html#T34" target="_self" title="INSTALG1:th.34">Th34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:44"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c12">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">o</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S9</font>,<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">h9</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c14">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E9:44"><span class="lab"><font color="Green" title="E30">A6</font></span></a>, <a class="txt" href="#E13:44"><span class="lab"><font color="Green" title="E33">A9</font></span></a>, <a class="txt" href="#E12:44"><span class="lab"><font color="Green" title="E32">A8</font></span></a>, <a class="txt" href="#E11:44"><span class="lab"><font color="Green" title="E31">A7</font></span></a>, <a class="ref" href="msualg_3.html#D9" title="MSUALG_3:def.9">MSUALG_3:def 9</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/>


</div>
