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<span class="kw">let </span><font color="Maroon" title="c1">X</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">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a><br/>  for <font color="Olive" title="b3">c</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Olive" title="b3">c</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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">c</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c2">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Olive" title="b1">c</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">c</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</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="c2">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span><br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:16_1"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> or <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T5" target="_self" onmouseover="rs('bspace/T5')" onmouseout="rh()">Th5</a>, <a class="ref" href="bspace.html#T6" target="_self" onmouseover="rs('bspace/T6')" onmouseout="rh()">Th6</a>, <a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1"><span class="kw">suppose </span></a><a NAME="E1:16_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span><br/><div class="add"><a NAME="E2:16_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#D4" target="_self" onmouseover="rs('bspace/D4')" onmouseout="rh()">Def4</a></span>;<br/><span class="kw">hence </span><a NAME="E3:16_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="bspace.html#D4" target="_self" onmouseover="rs('bspace/D4')" onmouseout="rh()">Def4</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_2"><span class="kw">suppose </span></a><a NAME="E1:16_1_2"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span><br/><div class="add"><a NAME="E2:16_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#D4" target="_self" onmouseover="rs('bspace/D4')" onmouseout="rh()">Def4</a></span>;<br/><span class="kw">hence </span><a NAME="E3:16_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bspace.html#K4" title="BSPACE:func.4">\*\</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_1_2"><span class="lab"><font color="Green" title="E11">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><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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