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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_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="E1:24_1_1_1"/>
(  not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  or <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  )
 </span>;<br/> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="msafree2.html#D10" onmouseover="rs('msafree2/D10')" onmouseout="rh()">MSAFREE2:def 10</a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:24_1_1_1_1"/>
 not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</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">b<sub>1</sub></font> being    <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> or  for <font color="Olive">b<sub>2</sub></font> being    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive">b<sub>1</sub></font>  holds <br/>(  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c3">X</font> or  ex <font color="Olive">b<sub>3</sub></font> being    <a href="msafree.html#M1" title="MSAFREE:mode.1">GeneratorSet</a> of <font color="Olive">b<sub>2</sub></font> st <font color="Olive">b<sub>3</sub></font> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a>  ) )</span><br/><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">S9</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" 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"> (  not <font color="Maroon" title="c4">S9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> or  for <font color="Olive">b<sub>1</sub></font> being    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c4">S9</font>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c3">X</font> or  ex <font color="Olive">b<sub>2</sub></font> being    <a href="msafree.html#M1" title="MSAFREE:mode.1">GeneratorSet</a> of <font color="Olive">b<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a>  ) )</span><br/><span class="kw">assume </span><a NAME="E2:24_1_1_1_1"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c4">S9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</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">b<sub>1</sub></font> being    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c4">S9</font>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c3">X</font> or  ex <font color="Olive">b<sub>2</sub></font> being    <a href="msafree.html#M1" title="MSAFREE:mode.1">GeneratorSet</a> of <font color="Olive">b<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">H</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c4">S9</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"> (  not <font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c3">X</font> or  ex <font color="Olive">b<sub>1</sub></font> being    <a href="msafree.html#M1" title="MSAFREE:mode.1">GeneratorSet</a> of <font color="Maroon" title="c5">H</font> st <font color="Olive">b<sub>1</sub></font> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a>  )</span><br/><span class="kw">assume </span><a NAME="E3:24_1_1_1_1"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c3">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">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="msafree.html#M1" title="MSAFREE:mode.1">GeneratorSet</a> of <font color="Maroon" title="c5">H</font> st <font color="Olive">b<sub>1</sub></font> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a> </span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">T</font> = <font color="Maroon" title="c3">X</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c5">H</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_1_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="msualg_2.html#D17" onmouseover="rs('msualg_2/D17')" onmouseout="rh()">MSUALG_2:def 17</a></span>;<br/><a NAME="E5:24_1_1_1_1"/>
 <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c6">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_1_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E3:24_1_1_1_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="extens_1.html#T18" onmouseover="rs('extens_1/T18')" onmouseout="rh()">EXTENS_1:18</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">T</font> = <font color="Maroon" title="c6">T</font> as    <a href="msafree.html#M1" title="MSAFREE:mode.1">GeneratorSet</a> of <font color="Maroon" title="c5">H</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_1_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E3:24_1_1_1_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="msafree.html#T3" onmouseover="rs('msafree/T3')" onmouseout="rh()">MSAFREE:3</a></span>;<br/><span class="kw">take </span>
<font color="Maroon" title="c7">T</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="c7">T</font> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a> </span><br/><span class="kw">thus </span><a NAME="E7:24_1_1_1_1"/>
<font color="Maroon" title="c7">T</font> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:24_1_1_1_2"/>
<font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</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">  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c3">X</font></span>)</span> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:24_1_1_1_2"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c3">X</font></span>)</span> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</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"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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