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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">F9</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/> for <font color="Olive" title="b3">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">I</font>,<font color="Olive" title="b1">F</font><br/> for <font color="Olive" title="b4">f9</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">I</font>,<font color="Olive" title="b2">F9</font>  st <font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b3">f</font> &amp; <font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Olive" title="b2">F9</font>,<font color="Olive" title="b4">f9</font> holds <br/><font color="Olive" title="b1">F</font> <a href="quofield.html#R2" title="QUOFIELD:pred.2">is_ringisomorph_to</a> <font color="Olive" title="b2">F9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">F9</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">F</font><br/> for <font color="Olive" title="b2">f9</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">F9</font>  st <font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Maroon" title="c2">F</font>,<font color="Olive" title="b1">f</font> &amp; <font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Maroon" title="c3">F9</font>,<font color="Olive" title="b2">f9</font> holds <br/><font color="Maroon" title="c2">F</font> <a href="quofield.html#R2" title="QUOFIELD:pred.2">is_ringisomorph_to</a> <font color="Maroon" title="c3">F9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f9</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">F9</font>  st <font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Maroon" title="c3">F9</font>,<font color="Olive" title="b1">f9</font> holds <br/><font color="Maroon" title="c2">F</font> <a href="quofield.html#R2" title="QUOFIELD:pred.2">is_ringisomorph_to</a> <font color="Maroon" title="c3">F9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">f9</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">F9</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Maroon" title="c3">F9</font>,<font color="Maroon" title="c5">f9</font> implies <font color="Maroon" title="c2">F</font> <a href="quofield.html#R2" title="QUOFIELD:pred.2">is_ringisomorph_to</a> <font color="Maroon" title="c3">F9</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:101"/><span class="lab"><font color="Green" title="E71">A1</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c4">f</font>
 <span class="kw">and </span><br/><a NAME="E2:101"/><span class="lab"><font color="Green" title="E72">A2</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="quofield.html#R3" title="QUOFIELD:pred.3">has_Field_of_Quotients_Pair</a> <font color="Maroon" title="c3">F9</font>,<font color="Maroon" title="c5">f9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> <a href="quofield.html#R2" title="QUOFIELD:pred.2">is_ringisomorph_to</a> <font color="Maroon" title="c3">F9</font></span><br/>

<a NAME="E3:101"/><span class="lab"><font color="Green" title="E73">A3</font></span>: 
<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">F9</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">f9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></span>;<br/>
<a NAME="E4:101"/><span class="lab"><font color="Green" title="E74">A4</font></span>: 
<font color="Maroon" title="c4">f</font> is  <a href="quofield.html#V3" title="QUOFIELD:attr.3">RingMonomorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:101"><span class="lab"><font color="Green" title="E71">A1</font></span></a>, <a class="ref" href="quofield.html#D29" target="_self" title="QUOFIELD:def.29">Def29</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">h2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">F9</font>,<font color="Maroon" title="c2">F</font><span class="kw"> such that </span><br/><a NAME="E6:101"/><span class="lab"><font color="Green" title="E75">A5</font></span>: 
( <font color="Maroon" title="c6">h2</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>  &amp; <font color="Maroon" title="c6">h2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> )
 <span class="kw">and </span><br/><a NAME="E7:101"/>
for <font color="Olive" title="b1">h9</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">F9</font>,<font color="Maroon" title="c2">F</font>  st <font color="Olive" title="b1">h9</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>  &amp; <font color="Olive" title="b1">h9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> holds <br/><font color="Olive" title="b1">h9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:101"><span class="lab"><font color="Green" title="E72">A2</font></span></a>, <a class="ref" href="quofield.html#D29" target="_self" title="QUOFIELD:def.29">Def29</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">h3</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c2">F</font><span class="kw"> such that </span><br/><a NAME="E9:101"/>
<font color="Maroon" title="c7">h3</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a> 
 <span class="kw">and </span><br/><a NAME="E10:101"/>
<font color="Maroon" title="c7">h3</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font>
 <span class="kw">and </span><br/><a NAME="E11:101"/><span class="lab"><font color="Green" title="E76">A6</font></span>: 
for <font color="Olive" title="b1">h9</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c2">F</font>  st <font color="Olive" title="b1">h9</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>  &amp; <font color="Olive" title="b1">h9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> holds <br/><font color="Olive" title="b1">h9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">h3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:101"><span class="lab"><font color="Green" title="E71">A1</font></span></a>, <a class="txt" href="#E4:101"><span class="lab"><font color="Green" title="E74">A4</font></span></a>, <a class="ref" href="quofield.html#D29" target="_self" title="QUOFIELD:def.29">Def29</a></span>;<br/>
<a NAME="E12:101"/><span class="lab"><font color="Green" title="E77">A7</font></span>: 
<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></span>;<br/>
<a NAME="E13:101"/><span class="lab"><font color="Green" title="E78">A8</font></span>: 
<font color="Maroon" title="c5">f9</font> is  <a href="quofield.html#V3" title="QUOFIELD:attr.3">RingMonomorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:101"><span class="lab"><font color="Green" title="E72">A2</font></span></a>, <a class="ref" href="quofield.html#D29" target="_self" title="QUOFIELD:def.29">Def29</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">h1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c3">F9</font><span class="kw"> such that </span><br/><a NAME="E15:101"/><span class="lab"><font color="Green" title="E79">A9</font></span>: 
<font color="Maroon" title="c8">h1</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a> 
 <span class="kw">and </span><br/><a NAME="E16:101"/><span class="lab"><font color="Green" title="E80">A10</font></span>: 
<font color="Maroon" title="c8">h1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">f9</font>
 <span class="kw">and </span><br/><a NAME="E17:101"/>
for <font color="Olive" title="b1">h9</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c3">F9</font>  st <font color="Olive" title="b1">h9</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>  &amp; <font color="Olive" title="b1">h9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">f9</font> holds <br/><font color="Olive" title="b1">h9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:101"><span class="lab"><font color="Green" title="E71">A1</font></span></a>, <a class="ref" href="quofield.html#D29" target="_self" title="QUOFIELD:def.29">Def29</a></span>;<br/>
<a NAME="E18:101"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c6">h2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">h1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c6">h2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">h1</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:101"><span class="lab"><font color="Green" title="E79">A9</font></span></a>, <a class="txt" href="#E16:101"><span class="lab"><font color="Green" title="E80">A10</font></span></a>, <a class="txt" href="#E6:101"><span class="lab"><font color="Green" title="E75">A5</font></span></a>, <a class="ref" href="quofield.html#T57" target="_self" title="QUOFIELD:th.57">Th57</a>, <a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E81">A11</font></span>: <font color="Maroon" title="c6">h2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">h1</font> = 
<font color="Maroon" title="c7">h3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:101"><span class="lab"><font color="Green" title="E76">A6</font></span></a></span>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">F</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:101"><span class="lab"><font color="Green" title="E77">A7</font></span></a>, <a class="txt" href="#E11:101"><span class="lab"><font color="Green" title="E76">A6</font></span></a></span>
;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">h3</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">F9</font>,<font color="Maroon" title="c3">F9</font><span class="kw"> such that </span><br/><a NAME="E21:101"/>
<font color="Maroon" title="c9">h3</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a> 
 <span class="kw">and </span><br/><a NAME="E22:101"/>
<font color="Maroon" title="c9">h3</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">f9</font>
 <span class="kw">and </span><br/><a NAME="E23:101"/><span class="lab"><font color="Green" title="E82">A12</font></span>: 
for <font color="Olive" title="b1">h9</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">F9</font>,<font color="Maroon" title="c3">F9</font>  st <font color="Olive" title="b1">h9</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>  &amp; <font color="Olive" title="b1">h9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">f9</font> holds <br/><font color="Olive" title="b1">h9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">h3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:101"><span class="lab"><font color="Green" title="E72">A2</font></span></a>, <a class="txt" href="#E13:101"><span class="lab"><font color="Green" title="E78">A8</font></span></a>, <a class="ref" href="quofield.html#D29" target="_self" title="QUOFIELD:def.29">Def29</a></span>;<br/>
<a NAME="E24:101"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c8">h1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">h2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">f9</font> &amp; <font color="Maroon" title="c8">h1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">h2</font> is  <a href="quofield.html#V1" title="QUOFIELD:attr.1">RingHomomorphism</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:101"><span class="lab"><font color="Green" title="E79">A9</font></span></a>, <a class="txt" href="#E16:101"><span class="lab"><font color="Green" title="E80">A10</font></span></a>, <a class="txt" href="#E6:101"><span class="lab"><font color="Green" title="E75">A5</font></span></a>, <a class="ref" href="quofield.html#T57" target="_self" title="QUOFIELD:th.57">Th57</a>, <a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c8">h1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">h2</font> = 
<font color="Maroon" title="c9">h3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:101"><span class="lab"><font color="Green" title="E82">A12</font></span></a></span>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">F9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101"><span class="lab"><font color="Green" title="E73">A3</font></span></a>, <a class="txt" href="#E23:101"><span class="lab"><font color="Green" title="E82">A12</font></span></a></span>
;<br/>
<a NAME="E26:101"/><span class="kw">then </span>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c8">h1</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">F9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T24" title="FUNCT_2:th.24">FUNCT_2:24</a></span>;<br/>
<a NAME="E27:101"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A13</font></span>: 
<font color="Maroon" title="c8">h1</font> is  <a href="quofield.html#V2" title="QUOFIELD:attr.2">RingEpimorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:101"><span class="lab"><font color="Green" title="E79">A9</font></span></a>, <a class="ref" href="quofield.html#D22" target="_self" title="QUOFIELD:def.22">Def22</a></span>;<br/>
<a NAME="E28:101"/>
<font color="Maroon" title="c8">h1</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:101"><span class="lab"><font color="Green" title="E81">A11</font></span></a>, <a class="ref" href="funct_2.html#T37" title="FUNCT_2:th.37">FUNCT_2:37</a></span>;<br/>
<a NAME="E29:101"/><span class="kw">then </span>
<font color="Maroon" title="c8">h1</font> is  <a href="quofield.html#V3" title="QUOFIELD:attr.3">RingMonomorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:101"><span class="lab"><font color="Green" title="E79">A9</font></span></a>, <a class="ref" href="quofield.html#D23" target="_self" title="QUOFIELD:def.23">Def23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E30:101"/>
<font color="Maroon" title="c2">F</font> <a href="quofield.html#R2" title="QUOFIELD:pred.2">is_ringisomorph_to</a> <font color="Maroon" title="c3">F9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:101"><span class="lab"><font color="Green" title="E83">A13</font></span></a>, <a class="ref" href="quofield.html#D26" target="_self" title="QUOFIELD:def.26">Def26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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