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<span class="kw">let </span><font color="Maroon" title="c1">U0</font> be   <a href="unialg_1.html#NM1" title="UNIALG_1:NM.1">Universal_Algebra</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">U1</font>, <font color="Olive" title="b2">U2</font> being   <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">strict</a>   <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c1">U0</font>  st  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">U1</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 <font color="Olive" title="b2">U2</font> holds <br/><font color="Olive" title="b1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">U2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">U1</font>, <font color="Maroon" title="c3">U2</font> be   <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">strict</a>   <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c1">U0</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"> (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</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 <font color="Maroon" title="c3">U2</font> implies <font color="Maroon" title="c2">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">U2</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:21"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</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 <font color="Maroon" title="c3">U2</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">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">U2</font></span><br/>

<a NAME="E2:21"/><span class="kw">then </span>
( <font color="Maroon" title="c2">U1</font> is   <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">strict</a>   <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c3">U2</font> &amp; <font color="Maroon" title="c3">U2</font> is   <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">strict</a>   <a href="unialg_2.html#M1" title="UNIALG_2:mode.1">SubAlgebra</a> of <font color="Maroon" title="c2">U1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#T11" target="_self" onmouseover="rs('unialg_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:21"/>
<font color="Maroon" title="c2">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">U2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#T10" target="_self" onmouseover="rs('unialg_2/T10')" onmouseout="rh()">Th10</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/>


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