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<span class="kw">let </span><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">S3</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">X</font> being <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</font><br/> for <font color="Olive" title="b2">f1</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="c1">S1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font><br/> for <font color="Olive" title="b3">g1</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b2">f1</font>,<font color="Olive" title="b3">g1</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b4">f2</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">S2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</font><br/> for <font color="Olive" title="b5">g2</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">f2</font>,<font color="Olive" title="b5">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> holds <br/> <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b5">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b3">g1</font></span>)</span>,<font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Olive" title="b4">f2</font>,<font color="Olive" title="b5">g2</font>,<font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b2">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Olive" title="b2">f1</font>,<font color="Olive" title="b3">g1</font>,<span class="p2">(<span class="default"><font color="Olive" title="b1">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b4">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">X</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</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">f1</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="c1">S1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font><br/> for <font color="Olive" title="b2">g1</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">g1</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b3">f2</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">S2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</font><br/> for <font color="Olive" title="b4">g2</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b3">f2</font>,<font color="Olive" title="b4">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> holds <br/> <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b2">g1</font></span>)</span>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Olive" title="b3">f2</font>,<font color="Olive" title="b4">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b3">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">f1</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="c1">S1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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"> for <font color="Olive" title="b1">g1</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon" title="c5">f1</font>,<font color="Olive" title="b1">g1</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b2">f2</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">S2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</font><br/> for <font color="Olive" title="b3">g2</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b2">f2</font>,<font color="Olive" title="b3">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> holds <br/> <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">g1</font></span>)</span>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Olive" title="b2">f2</font>,<font color="Olive" title="b3">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Olive" title="b1">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b2">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">g1</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="c5">f1</font>,<font color="Maroon" title="c6">g1</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> implies for <font color="Olive" title="b1">f2</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">S2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</font><br/> for <font color="Olive" title="b2">g2</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f2</font>,<font color="Olive" title="b2">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> holds <br/> <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Olive" title="b1">f2</font>,<font color="Olive" title="b2">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:57"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<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"> for <font color="Olive" title="b1">f2</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">S2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</font><br/> for <font color="Olive" title="b2">g2</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f2</font>,<font color="Olive" title="b2">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> holds <br/> <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Olive" title="b1">f2</font>,<font color="Olive" title="b2">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">f2</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">S2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S3</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">g2</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon" title="c7">f2</font>,<font color="Olive" title="b1">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> holds <br/> <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c7">f2</font>,<font color="Olive" title="b1">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">g2</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="c7">f2</font>,<font color="Maroon" title="c8">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> implies  <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c9">f</font> = <font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">g</font> = <font color="Maroon" title="c8">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font>;<br/>
<span class="kw">assume </span><a NAME="E2:57"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">Af</font> = <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span>, <font color="Maroon" title="c12">Af1</font> = <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font> as   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="instalg1.html#T23" target="_self" title="INSTALG1:th.23">Th23</a>, <a class="ref" href="pua2mss1.html#T30" title="PUA2MSS1:th.30">PUA2MSS1:30</a></span>;<br/>
<a NAME="E4:57"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
 <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="instalg1.html#D5" target="_self" title="INSTALG1:def.5">Def5</a></span>;<br/>
<a NAME="E5:57"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span></span>)</span> <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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c13">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pzfmisc1.html#D3" title="PZFMISC1:def.3">PZFMISC1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c13">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> or  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:57_1"/>
<font color="Maroon" title="c13">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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"> (  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">s</font> = <font color="Maroon" title="c13">i</font> as   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c2">S2</font> ;<br/>
<a NAME="E3:57_1"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p2">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="instalg1.html#D3" target="_self" title="INSTALG1:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:57_1"/>
(  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E6:57"/>
<span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="instalg1.html#T28" target="_self" title="INSTALG1:th.28">Th28</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">hf1</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c12">Af1</font>,<font color="Maroon" title="c11">Af</font><span class="kw"> such that </span><br/><a NAME="E8:57"/><span class="lab"><font color="Green" title="E35">A5</font></span>: 
<font color="Maroon" title="c13">hf1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font>
 <span class="kw">and </span><br/><a NAME="E9:57"/><span class="lab"><font color="Green" title="E36">A6</font></span>: 
<font color="Maroon" title="c13">hf1</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c12">Af1</font>,<font color="Maroon" title="c11">Af</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E4:57"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="txt" href="#E5:57"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="instalg1.html#T35" target="_self" title="INSTALG1:th.35">Th35</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">hh</font> =  <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> as   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c12">Af1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">hf1h</font> = <font color="Maroon" title="c13">hf1</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c14">hh</font> as   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span></span>)</span> ;<br/>
<a NAME="E12:57"/><span class="lab"><font color="Green" title="E37">A7</font></span>: 
<font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E38">A8</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c16">s</font> be   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</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">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c15">hf1h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Maroon" title="c16">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">s</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c17">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s</font>; <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="c15">hf1h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c16">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">s</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c18">t</font> =  <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c16">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="msaterm.html#T4" title="MSATERM:th.4">MSATERM:4</a></span>;<br/><a NAME="E2:57_2"/><span class="lab"><font color="Green" title="E39">A9</font></span>: 
 <a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# <span class="p1">(<span class="default"><a href="msafree.html#K9" title="MSAFREE:func.9">FreeSort</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeOper</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span></span>)</span> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msafree.html#D16" title="MSAFREE:def.16">MSAFREE:def 16</a></span>;<br/><a NAME="E3:57_2"/>
(  <a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <font color="Maroon" title="c18">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s</font> &amp; <span class="p1">(<span class="default"><a href="msafree.html#K9" title="MSAFREE:func.9">FreeSort</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msafree.html#K8" title="MSAFREE:func.8">FreeSort</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span>,<font color="Maroon" title="c16">s</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msafree.html#D13" title="MSAFREE:def.13">MSAFREE:def 13</a>, <a class="ref" href="msaterm.html#T14" title="MSATERM:th.14">MSATERM:14</a></span>;<br/><a NAME="E4:57_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A10</font></span>: 
 <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c16">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57_2"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="msaterm.html#D5" title="MSATERM:def.5">MSATERM:def 5</a></span>;<br/><a NAME="E5:57_2"/><span class="lab"><font color="Green" title="E41">A11</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:57"><span class="lab"><font color="Green" title="E37">A7</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c15">hf1h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c16">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">hf1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c16">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#T2" title="MSUALG_3:th.2">MSUALG_3:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">hf1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></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"><span class="p3">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c16">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:57"><span class="lab"><font color="Green" title="E37">A7</font></span></a>, <a class="txt" href="#E4:57_2"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">hf1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">s</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E12:57"><span class="lab"><font color="Green" title="E37">A7</font></span></a>, <a class="ref" href="instalg1.html#D5" target="_self" title="INSTALG1:def.5">Def5</a></span>
;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c15">hf1h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c16">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">s</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:57"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
<br/>.= 
 <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">s</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E5:57_2"><span class="lab"><font color="Green" title="E41">A11</font></span></a>, <a class="ref" href="instalg1.html#D5" target="_self" title="INSTALG1:def.5">Def5</a></span>
<br/>.= 
 <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">s</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E14:57"/><span class="lab"><font color="Green" title="E39">A12</font></span>: 
<font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c8">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="pua2mss1.html#T30" title="PUA2MSS1:th.30">PUA2MSS1:30</a></span>;<br/>
<a NAME="E15:57"/>
 <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="instalg1.html#D5" target="_self" title="INSTALG1:def.5">Def5</a></span>;<br/>
<a NAME="E16:57"/><span class="kw">then </span>
<font color="Maroon" title="c13">hf1</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c14">hh</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="msafree.html#K12" title="MSAFREE:func.12">FreeMSA</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">Af</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:57"><span class="lab"><font color="Green" title="E36">A6</font></span></a>, <a class="txt" href="#E12:57"><span class="lab"><font color="Green" title="E37">A7</font></span></a>, <a class="ref" href="msualg_3.html#T10" title="MSUALG_3:th.10">MSUALG_3:10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:57"/>
 <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c7">f2</font>,<font color="Maroon" title="c8">g2</font>,<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">g1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f2</font></span>)</span>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:57"><span class="lab"><font color="Green" title="E39">A12</font></span></a>, <a class="txt" href="#E8:57"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="txt" href="#E13:57"><span class="lab"><font color="Green" title="E38">A8</font></span></a>, <a class="ref" href="instalg1.html#D5" target="_self" title="INSTALG1:def.5">Def5</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>
