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<span class="kw">let </span><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c3">X3</font> be   <a href="stacks_1.html#NM3" title="STACKS_1:NM.3">StackAlgebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font> <a href="stacks_1.html#R4" title="STACKS_1:pred.4">are_isomorphic</a>  &amp; <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">X3</font> <a href="stacks_1.html#R4" title="STACKS_1:pred.4">are_isomorphic</a>  implies <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X3</font> <a href="stacks_1.html#R4" title="STACKS_1:pred.4">are_isomorphic</a>  )</span><br/>





<span class="kw">given </span><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">G1</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><a NAME="E2:90"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">G1</font> <a href="stacks_1.html#R3" title="STACKS_1:pred.3">form_isomorphism_between</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="stacks_1.html#D22" target="_self" title="STACKS_1:def.22">STACKS_1:def 22</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">X3</font> <a href="stacks_1.html#R4" title="STACKS_1:pred.4">are_isomorphic</a>  or <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X3</font> <a href="stacks_1.html#R4" title="STACKS_1:pred.4">are_isomorphic</a>  )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c6">F2</font>, <font color="Maroon" title="c7">G2</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><a NAME="E4:90"/><span class="lab"><font color="Green" title="E62">A2</font></span>: 
<font color="Maroon" title="c6">F2</font>,<font color="Maroon" title="c7">G2</font> <a href="stacks_1.html#R3" title="STACKS_1:pred.3">form_isomorphism_between</a> <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">X3</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="stacks_1.html#D22" target="_self" title="STACKS_1:def.22">STACKS_1:def 22</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X3</font> <a href="stacks_1.html#R4" title="STACKS_1:pred.4">are_isomorphic</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c6">F2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">F1</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="stacks_1.html#D22" target="_self" title="STACKS_1:def.22">STACKS_1:def 22</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <font color="Maroon" title="c6">F2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">F1</font>,<font color="Olive" title="b1">G</font> <a href="stacks_1.html#R3" title="STACKS_1:pred.3">form_isomorphism_between</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X3</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c7">G2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">G1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">F2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c7">G2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">G1</font> <a href="stacks_1.html#R3" title="STACKS_1:pred.3">form_isomorphism_between</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X3</font></span><br/>

<span class="kw">thus </span><a NAME="E5:90"/>
<font color="Maroon" title="c6">F2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c7">G2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">G1</font> <a href="stacks_1.html#R3" title="STACKS_1:pred.3">form_isomorphism_between</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:90"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="txt" href="#E4:90"><span class="lab"><font color="Green" title="E62">A2</font></span></a>, <a class="ref" href="stacks_1.html#T44" target="_self" title="STACKS_1:th.44">Th90</a></span>; <a class="txt" 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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