<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">q</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="group_7.html#V2" title="GROUP_7:attr.2">Group-like</a>   <a href="group_7.html#V3" title="GROUP_7:attr.3">associative</a>  <a href="group_7.html#NM1" title="GROUP_7:NM.1">multMagma-Family</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span><br/>  for <font color="Olive" title="b2">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b2">G</font> holds <br/> ex <font color="Olive" title="b3">HFG</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Olive" title="b1">F</font></span>)</span>,<font color="Olive" title="b2">G</font> st <br/>( <font color="Olive" title="b3">HFG</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b4">x</font> being  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds  <font color="Olive" title="b3">HFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Olive" title="b4">x</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="group_7.html#V2" title="GROUP_7:attr.2">Group-like</a>   <a href="group_7.html#V3" title="GROUP_7:attr.3">associative</a>  <a href="group_7.html#NM1" title="GROUP_7:NM.1">multMagma-Family</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>  st <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b1">G</font> holds <br/> ex <font color="Olive" title="b2">HFG</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span>,<font color="Olive" title="b1">G</font> st <br/>( <font color="Olive" title="b2">HFG</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b3">x</font> being  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds  <font color="Olive" title="b2">HFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Olive" title="b3">x</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">G</font> implies  ex <font color="Olive" title="b1">HFG</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span>,<font color="Maroon" title="c3">G</font> st <br/>( <font color="Olive" title="b1">HFG</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b2">x</font> being  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds  <font color="Olive" title="b1">HFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Olive" title="b2">x</font> ) ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:34"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">G</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">HFG</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span>,<font color="Maroon" title="c3">G</font> st <br/>( <font color="Olive" title="b1">HFG</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b2">x</font> being  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds  <font color="Olive" title="b1">HFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Olive" title="b2">x</font> ) )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">I</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c3">G</font>,<span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:34"/><span class="lab"><font color="Green" title="E36">A2</font></span>: 
( <font color="Maroon" title="c4">I</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">G</font> holds  <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b1">x</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_17.html#T21" target="_self" onmouseover="rs('group_17/T21')" onmouseout="rh()">Th21</a>, <a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E35">A1</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">HFG</font> = <font color="Maroon" title="c4">I</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> ;<br/>
<a NAME="E4:34"/><span class="lab"><font color="Green" title="E37">A3</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="funct_2.html#D3" onmouseover="rs('funct_2/D3')" onmouseout="rh()">FUNCT_2:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">HFG</font> = <font color="Maroon" title="c4">I</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span>,<font color="Maroon" title="c3">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T25" onmouseover="rs('funct_2/T25')" onmouseout="rh()">FUNCT_2:25</a>, <a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E36">A2</font></span></a></span>;<br/>
<a NAME="E6:34"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
( <font color="Maroon" title="c6">HFG</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">I</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G</font> &amp; <font color="Maroon" title="c4">I</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">HFG</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E4:34"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="ref" href="funct_2.html#T29" onmouseover="rs('funct_2/T29')" onmouseout="rh()">FUNCT_2:29</a></span>;<br/>
<a NAME="E7:34"/><span class="lab"><font color="Green" title="E39">A5</font></span>: 
<font color="Maroon" title="c6">HFG</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:34"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="funct_2.html#T23" onmouseover="rs('funct_2/T23')" onmouseout="rh()">FUNCT_2:23</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">HFG</font> = <font color="Maroon" title="c6">HFG</font> as   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span>,<font color="Maroon" title="c3">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="group_6.html#T62" onmouseover="rs('group_6/T62')" onmouseout="rh()">GROUP_6:62</a></span>;<br/>
<a NAME="E9:34"/>
 for <font color="Olive" title="b1">y</font> being  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds  <font color="Maroon" title="c7">HFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Olive" title="b1">y</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="34_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">y</font> be  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">HFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Maroon" title="c8">y</font></span><br/>

<a NAME="E1:34_1"/><span class="lab"><font color="Green" title="E40">A6</font></span>: 
( <font color="Maroon" title="c8">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span> &amp; <font color="Maroon" title="c8">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G</font> &amp; <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">q</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="group_17.html#T25" target="_self" onmouseover="rs('group_17/T25')" onmouseout="rh()">Th25</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">z</font> = <font color="Maroon" title="c8">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="group_17.html#T25" target="_self" onmouseover="rs('group_17/T25')" onmouseout="rh()">Th25</a></span>;<br/>
<span class="lab"><font color="Green" title="E41">A7</font></span>: <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">z</font> = 
<font color="Maroon" title="c1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c9">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E36">A2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c8">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="group_17.html#T25" target="_self" onmouseover="rs('group_17/T25')" onmouseout="rh()">Th25</a></span>
;<br/>
<span class="kw">thus </span><font color="Maroon" title="c7">HFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> = 
<font color="Maroon" title="c9">z</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T26" onmouseover="rs('funct_2/T26')" onmouseout="rh()">FUNCT_2:26</a>, <a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E3:34_1"><span class="lab"><font color="Green" title="E41">A7</font></span></a></span>
<br/>.= 
 <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Maroon" title="c8">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_17.html#T9" target="_self" onmouseover="rs('group_17/T9')" onmouseout="rh()">Th9</a>, <a class="txt" href="#E1:34_1"><span class="lab"><font color="Green" title="E40">A6</font></span></a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E10:34"/>
 ex <font color="Olive" title="b1">HFG</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c2">F</font></span>)</span>,<font color="Maroon" title="c3">G</font> st <br/>( <font color="Olive" title="b1">HFG</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b2">x</font> being  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds  <font color="Olive" title="b1">HFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Olive" title="b2">x</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:34"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E36">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
