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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a> <a href="mod_2.html#NM1" title="MOD_2:NM.1">LModMorphism</a> of <font color="Maroon" title="c1">R</font>  st  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Olive" title="b1">f</font> holds <br/> ex <font color="Olive" title="b3">G1</font>, <font color="Olive" title="b4">G2</font>, <font color="Olive" title="b5">G3</font> being  <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font> ex <font color="Olive" title="b6">f0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b3">G1</font>,<font color="Olive" title="b4">G2</font> ex <font color="Olive" title="b7">g0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b4">G2</font>,<font color="Olive" title="b5">G3</font> st <br/>( <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b3">G1</font>,<font color="Olive" title="b4">G2</font>,<font color="Olive" title="b6">f0</font> #) &amp; <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b4">G2</font>,<font color="Olive" title="b5">G3</font>,<font color="Olive" title="b7">g0</font> #) &amp; <font color="Olive" title="b2">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b3">G1</font>,<font color="Olive" title="b5">G3</font>,<span class="p1">(<span class="default"><font color="Olive" title="b7">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b6">f0</font></span>)</span> #) )</span><br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be  <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a> <a href="mod_2.html#NM1" title="MOD_2:NM.1">LModMorphism</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font> implies  ex <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being  <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font> ex <font color="Olive" title="b4">f0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font> ex <font color="Olive" title="b5">g0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font> st <br/>( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font>,<font color="Olive" title="b4">f0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font>,<font color="Olive" title="b5">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b3">G3</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f0</font></span>)</span> #) ) )</span><br/>



<b>assume </b><a NAME="E1:32"/><i><font color="Green" title="E20">A1</font></i>: 
 <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being  <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font> ex <font color="Olive" title="b4">f0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font> ex <font color="Olive" title="b5">g0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font> st <br/>( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font>,<font color="Olive" title="b4">f0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font>,<font color="Olive" title="b5">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b3">G3</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f0</font></span>)</span> #) )</span><br/>

<b>set </b><font color="Maroon" title="c4">G1</font> =  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font>;<br/>
<b>set </b><font color="Maroon" title="c5">G2</font> =  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font>;<br/>
<b>set </b><font color="Maroon" title="c6">G3</font> =  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">f'</font> = <font color="Maroon" title="c2">f</font> as  <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a>  <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font>, <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font> <b>by </b><i><a class="ref" href="mod_2.html#D11" target="_self" title="MOD_2:def.11">Def11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">g'</font> = <font color="Maroon" title="c3">g</font> as  <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a>  <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font>, <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font> <b>by </b><i><a class="txt" href="mod_2.html#E1:32"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="mod_2.html#D11" target="_self" title="MOD_2:def.11">Def11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">f0</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span><b> such that </b><br/><a NAME="E5:32"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c7">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c9">f0</font> #)
 ;<br/>
<b>consider </b><font color="Maroon" title="c10">g0</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span><b> such that </b><br/><a NAME="E7:32"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c8">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<font color="Maroon" title="c10">g0</font> #)
 <b>by </b><i><a class="ref" href="mod_2.html#T15" target="_self" title="MOD_2:th.15">Th15</a></i>;<br/>
<b>take </b>
 <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G2</font>, <font color="Olive" title="b2">G3</font> being  <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font> ex <font color="Olive" title="b3">f0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Olive" title="b1">G2</font> ex <font color="Olive" title="b4">g0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">G2</font>,<font color="Olive" title="b2">G3</font> st <br/>( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Olive" title="b1">G2</font>,<font color="Olive" title="b3">f0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Olive" title="b1">G2</font>,<font color="Olive" title="b2">G3</font>,<font color="Olive" title="b4">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Olive" title="b2">G3</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">f0</font></span>)</span> #) )</span><br/>

<b>take </b>
 <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G3</font> being  <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font> ex <font color="Olive" title="b2">f0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> ex <font color="Olive" title="b3">g0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Olive" title="b1">G3</font> st <br/>( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Olive" title="b2">f0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Olive" title="b1">G3</font>,<font color="Olive" title="b3">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Olive" title="b1">G3</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">f0</font></span>)</span> #) )</span><br/>

<b>take </b>
 <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> ex <font color="Olive" title="b2">g0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span> st <br/>( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Olive" title="b1">f0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<font color="Olive" title="b2">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f0</font></span>)</span> #) )</span><br/>

<b>take </b>
<font color="Maroon" title="c9">f0</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">g0</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span> st <br/>( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c9">f0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<font color="Olive" title="b1">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">f0</font></span>)</span> #) )</span><br/>

<b>take </b>
<font color="Maroon" title="c10">g0</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c9">f0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<font color="Maroon" title="c10">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">f0</font></span>)</span> #) )</span><br/>

<b>thus </b><a NAME="E8:32"/>
( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c9">f0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<font color="Maroon" title="c10">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <span class="p1">(<span class="default"><a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">f0</font></span>)</span> #) )
 <b>by </b><i><a class="txt" href="mod_2.html#E5:32"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="mod_2.html#E7:32"><i><font color="Green" title="E22">A3</font></i></a>, <a class="ref" href="mod_2.html#T21" target="_self" title="MOD_2:th.21">Th21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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