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

<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <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">  for <font color="Olive" title="b1">h</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font><br/>  for <font color="Olive" title="b2">G1</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b3">G2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b4">H1</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Olive" title="b1">h</font><br/>  for <font color="Olive" title="b5">H2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Olive" title="b1">h</font>  st <font color="Olive" title="b3">G2</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b2">G1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Olive" title="b2">G1</font>,<font color="Olive" title="b3">G2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b3">G2</font></span>)</span> &amp; <font color="Olive" title="b4">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b5">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b3">G2</font> holds <br/><font color="Olive" title="b4">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Olive" title="b4">H1</font>,<font color="Olive" title="b5">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Olive" title="b1">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b5">H2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">h</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</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">  for <font color="Olive" title="b1">G1</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">G2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b3">H1</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font><br/>  for <font color="Olive" title="b4">H2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font>  st <font color="Olive" title="b2">G2</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Olive" title="b1">G1</font> &amp; <font color="Olive" title="b1">G1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b2">G2</font></span>)</span> &amp; <font color="Olive" title="b3">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b1">G1</font> &amp; <font color="Olive" title="b4">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b2">G2</font> holds <br/><font color="Olive" title="b3">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Olive" title="b3">H1</font>,<font color="Olive" title="b4">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b4">H2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">G1</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">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">  for <font color="Olive" title="b1">G2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">H1</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font><br/>  for <font color="Olive" title="b3">H2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font>  st <font color="Olive" title="b1">G2</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">G1</font> &amp; <font color="Maroon" title="c4">G1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">G1</font>,<font color="Olive" title="b1">G2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b1">G2</font></span>)</span> &amp; <font color="Olive" title="b2">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">G1</font> &amp; <font color="Olive" title="b3">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b1">G2</font> holds <br/><font color="Olive" title="b2">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Olive" title="b2">H1</font>,<font color="Olive" title="b3">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b3">H2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">G2</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">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">  for <font color="Olive" title="b1">H1</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font><br/>  for <font color="Olive" title="b2">H2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font>  st <font color="Maroon" title="c5">G2</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">G1</font> &amp; <font color="Maroon" title="c4">G1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c5">G2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c5">G2</font></span>)</span> &amp; <font color="Olive" title="b1">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">G1</font> &amp; <font color="Olive" title="b2">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c5">G2</font> holds <br/><font color="Olive" title="b1">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Olive" title="b1">H1</font>,<font color="Olive" title="b2">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b2">H2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">H1</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</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">  for <font color="Olive" title="b1">H2</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font>  st <font color="Maroon" title="c5">G2</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">G1</font> &amp; <font color="Maroon" title="c4">G1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c5">G2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c5">G2</font></span>)</span> &amp; <font color="Maroon" title="c6">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">G1</font> &amp; <font color="Olive" title="b1">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c5">G2</font> holds <br/><font color="Maroon" title="c6">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">H1</font>,<font color="Olive" title="b1">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b1">H2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">H2</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</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"> ( <font color="Maroon" title="c5">G2</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">G1</font> &amp; <font color="Maroon" title="c4">G1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c5">G2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c5">G2</font></span>)</span> &amp; <font color="Maroon" title="c6">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">G1</font> &amp; <font color="Maroon" title="c7">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c5">G2</font> implies <font color="Maroon" title="c6">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">H1</font>,<font color="Maroon" title="c7">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
<font color="Maroon" title="c5">G2</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">G1</font>
 <span class="kw">and </span><br/><a NAME="E2:36"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c4">G1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c5">G2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c5">G2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:36"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
( <font color="Maroon" title="c6">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">G1</font> &amp; <font color="Maroon" title="c7">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c5">G2</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"> <font color="Maroon" title="c6">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">H1</font>,<font color="Maroon" title="c7">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span></span><br/>

<a NAME="E4:36"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
<font color="Maroon" title="c7">H2</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c6">H1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="grsolv_1.html#T12" onmouseover="rs('grsolv_1/T12')" onmouseout="rh()">GRSOLV_1:12</a></span>;<br/>
<a NAME="E5:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A5</font></span>: 
(<font color="Maroon" title="c6">H1</font>,<font color="Maroon" title="c7">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a>  <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c7">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D1" onmouseover="rs('group_6/D1')" onmouseout="rh()">GROUP_6:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">I</font> = <font color="Maroon" title="c7">H2</font> as   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c6">H1</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">J</font> = <font color="Maroon" title="c6">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">H1</font>,<font color="Maroon" title="c7">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> as    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="ref" href="group_6.html#T28" onmouseover="rs('group_6/T28')" onmouseout="rh()">GROUP_6:28</a></span>;<br/>
<a NAME="E8:36"/>
 for <font color="Olive" title="b1">T</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span>  st <font color="Olive" title="b1">T</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c9">J</font> holds <br/><font color="Olive" title="b1">T</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">T</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</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"> ( <font color="Maroon" title="c10">T</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c9">J</font> implies <font color="Maroon" title="c10">T</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:36_1"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
<font color="Maroon" title="c10">T</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c9">J</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"> <font color="Maroon" title="c10">T</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span></span><br/>

<a NAME="E2:36_1"/>
 for <font color="Olive" title="b1">S</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span> holds  <font color="Olive" title="b1">S</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">T</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">S</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c11">S</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</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"> <font color="Maroon" title="c11">S</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">T</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">S</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c12">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:36_1_1"/><span class="lab"><font color="Green" title="E32">A7</font></span>: 
( <font color="Maroon" title="c11">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">g</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font> &amp; <font color="Maroon" title="c11">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">H2</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c12">g</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T21" onmouseover="rs('group_6/T21')" onmouseout="rh()">GROUP_6:21</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">h1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c6">H1</font><span class="kw"> such that </span><br/><a NAME="E4:36_1_1"/><span class="lab"><font color="Green" title="E33">A8</font></span>: 
( <font color="Maroon" title="c10">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">h1</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c8">I</font> &amp; <font color="Maroon" title="c10">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">I</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c13">h1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="ref" href="group_6.html#T23" onmouseover="rs('group_6/T23')" onmouseout="rh()">GROUP_6:23</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">h2</font> = <font color="Maroon" title="c13">h1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/>
<a NAME="E6:36_1_1"/><span class="lab"><font color="Green" title="E34">A9</font></span>: 
(  <a href="group_6.html#K6" title="GROUP_6:func.6">@</a> <font color="Maroon" title="c11">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">S</font> &amp;  <a href="group_6.html#K6" title="GROUP_6:func.6">@</a> <font color="Maroon" title="c10">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">T</font> &amp; <font color="Maroon" title="c13">h1</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">h2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T2" onmouseover="rs('group_6/T2')" onmouseout="rh()">GROUP_6:2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E35">A10</font></span>: <font color="Maroon" title="c11">S</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">T</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">h2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_1"><span class="lab"><font color="Green" title="E32">A7</font></span></a>, <a class="txt" href="#E4:36_1_1"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="ref" href="group_6.html#D3" onmouseover="rs('group_6/D3')" onmouseout="rh()">GROUP_6:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c14">h2</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_11.html#T1" onmouseover="rs('group_11/T1')" onmouseout="rh()">GROUP_11:1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E36">A11</font></span>: <font color="Maroon" title="c10">T</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">S</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">h2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_1"><span class="lab"><font color="Green" title="E32">A7</font></span></a>, <a class="txt" href="#E4:36_1_1"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E6:36_1_1"><span class="lab"><font color="Green" title="E34">A9</font></span></a>, <a class="ref" href="group_6.html#D3" onmouseover="rs('group_6/D3')" onmouseout="rh()">GROUP_6:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">h2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">g</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_11.html#T1" onmouseover="rs('group_11/T1')" onmouseout="rh()">GROUP_11:1</a></span>
;<br/>
<a NAME="E9:36_1_1"/>
<font color="Maroon" title="c12">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D5" onmouseover="rs('struct_0/D5')" onmouseout="rh()">STRUCT_0:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E11:36_1_1"/><span class="lab"><font color="Green" title="E37">A12</font></span>: 
<font color="Maroon" title="c12">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T45" onmouseover="rs('group_6/T45')" onmouseout="rh()">GROUP_6:45</a></span>;<br/>
<a NAME="E12:36_1_1"/><span class="lab"><font color="Green" title="E38">A13</font></span>: 
<font color="Maroon" title="c15">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D5" onmouseover="rs('struct_0/D5')" onmouseout="rh()">STRUCT_0:def 5</a></span>;<br/>
<a NAME="E13:36_1_1"/>
<font color="Maroon" title="c13">h1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">H1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D5" onmouseover="rs('struct_0/D5')" onmouseout="rh()">STRUCT_0:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">a1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">G1</font><span class="kw"> such that </span><br/><a NAME="E15:36_1_1"/><span class="lab"><font color="Green" title="E39">A14</font></span>: 
<font color="Maroon" title="c13">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K1" title="GRSOLV_1:func.1">|</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="group_6.html#T45" onmouseover="rs('group_6/T45')" onmouseout="rh()">GROUP_6:45</a></span>;<br/>
<a NAME="E16:36_1_1"/><span class="lab"><font color="Green" title="E40">A15</font></span>: 
<font color="Maroon" title="c16">a1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c4">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D5" onmouseover="rs('struct_0/D5')" onmouseout="rh()">STRUCT_0:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">a2</font> = <font color="Maroon" title="c16">a1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/>
<a NAME="E18:36_1_1"/><span class="lab"><font color="Green" title="E41">A16</font></span>: 
<font color="Maroon" title="c14">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:36_1_1"><span class="lab"><font color="Green" title="E39">A14</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E42">A17</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c14">h2</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">a2</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c5">G2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:36_1_1"><span class="lab"><font color="Green" title="E37">A12</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="grnilp_1.html#T24" target="_self" onmouseover="rs('grnilp_1/T24')" onmouseout="rh()">Th24</a></span>
<br/>.= 
<font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">a2</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grnilp_1.html#T23" target="_self" onmouseover="rs('grnilp_1/T23')" onmouseout="rh()">Th23</a></span>
;<br/>
<span class="lab"><font color="Green" title="E43">A18</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c14">h2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">g</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">a2</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c5">G2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:36_1_1"><span class="lab"><font color="Green" title="E37">A12</font></span></a>, <a class="txt" href="#E18:36_1_1"><span class="lab"><font color="Green" title="E41">A16</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="grnilp_1.html#T24" target="_self" onmouseover="rs('grnilp_1/T24')" onmouseout="rh()">Th24</a></span>
<br/>.= 
<font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grnilp_1.html#T23" target="_self" onmouseover="rs('grnilp_1/T23')" onmouseout="rh()">Th23</a></span>
;<br/>
<a NAME="E21:36_1_1"/><span class="lab"><font color="Green" title="E44">A19</font></span>: 
<span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">G1</font>,<span class="p2">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c5">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="grnilp_1.html#T19" target="_self" onmouseover="rs('grnilp_1/T19')" onmouseout="rh()">Th19</a></span>;<br/>
<a NAME="E22:36_1_1"/>
<span class="p1"><a href="group_5.html#K2" title="GROUP_5:func.2">[.</a><span class="default"><font color="Maroon" title="c17">a2</font>,<font color="Maroon" title="c15">a</font></span><a href="group_5.html#K2" title="GROUP_5:func.2">.]</a></span> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">G1</font>,<span class="p2">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:36_1_1"><span class="lab"><font color="Green" title="E38">A13</font></span></a>, <a class="txt" href="#E16:36_1_1"><span class="lab"><font color="Green" title="E40">A15</font></span></a>, <a class="ref" href="group_5.html#T65" onmouseover="rs('group_5/T65')" onmouseout="rh()">GROUP_5:65</a></span>;<br/>
<a NAME="E23:36_1_1"/><span class="kw">then </span>
<span class="p1"><a href="group_5.html#K2" title="GROUP_5:func.2">[.</a><span class="default"><font color="Maroon" title="c17">a2</font>,<font color="Maroon" title="c15">a</font></span><a href="group_5.html#K2" title="GROUP_5:func.2">.]</a></span> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1_1"><span class="lab"><font color="Green" title="E44">A19</font></span></a>, <a class="ref" href="group_2.html#T40" onmouseover="rs('group_2/T40')" onmouseout="rh()">GROUP_2:40</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">a2</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">a2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="group_5.html#K2" title="GROUP_5:func.2">[.</a><span class="default"><font color="Maroon" title="c17">a2</font>,<font color="Maroon" title="c15">a</font></span><a href="group_5.html#K2" title="GROUP_5:func.2">.]</a></span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T113" onmouseover="rs('group_2/T113')" onmouseout="rh()">GROUP_2:113</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">a2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_5.html#T16" onmouseover="rs('group_5/T16')" onmouseout="rh()">GROUP_5:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">a2</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T32" onmouseover="rs('group_2/T32')" onmouseout="rh()">GROUP_2:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">a2</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D5" onmouseover="rs('group_1/D5')" onmouseout="rh()">GROUP_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" onmouseover="rs('group_1/D4')" onmouseout="rh()">GROUP_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D5" onmouseover="rs('group_1/D5')" onmouseout="rh()">GROUP_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">a</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c5">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" onmouseover="rs('group_1/D4')" onmouseout="rh()">GROUP_1:def 4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E25:36_1_1"/>
<font color="Maroon" title="c11">S</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">T</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36_1_1"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="txt" href="#E8:36_1_1"><span class="lab"><font color="Green" title="E36">A11</font></span></a>, <a class="txt" href="#E19:36_1_1"><span class="lab"><font color="Green" title="E42">A17</font></span></a>, <a class="txt" href="#E20:36_1_1"><span class="lab"><font color="Green" title="E43">A18</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="E3:36_1"/>
<font color="Maroon" title="c10">T</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_5.html#T77" onmouseover="rs('group_5/T77')" onmouseout="rh()">GROUP_5:77</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="E9:36"/>
<font color="Maroon" title="c6">H1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">H1</font>,<font color="Maroon" title="c7">H2</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c7">H2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T58" onmouseover="rs('group_2/T58')" onmouseout="rh()">GROUP_2:58</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>
