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File:StrictContent/ArithmeticAlgebraLogic/forall/rec-forall4
CVS-ID:
Author:MathML 2 Recomendation
Description:forall/exists/and/plus

passed (p) failed (f) not-tested (n) broken-test (b) some parts pass (s)

Sample Rendering:

Created by: webeq

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forall n implies in n suchthat R lambda n and gt n 0 in n Z exists x y z and in x y z suchthat R lambda x y z and in x Z in y Z in z Z eq plus power x n power y n power z n

Source Code:

<math xmlns="http://www.w3.org/1998/Math/MathML">
         <bind>
            <csymbol cd="quant1">forall</csymbol>
            <bvar>
               <ci>n</ci>
            </bvar>
            <apply>
               <csymbol cd="logic1">implies</csymbol>
               <apply>
                  <csymbol cd="set1">in</csymbol>
                  <ci>n</ci>
                  <apply>
                     <csymbol cd="set1">suchthat</csymbol>
                     <ci>R</ci>
                     <bind>
                        <csymbol cd="fns1">lambda</csymbol>
                        <bvar>
                           <ci>n</ci>
                        </bvar>
                        <apply>
                           <csymbol cd="logic1">and</csymbol>
                           <apply>
                              <csymbol cd="relation1">gt</csymbol>
                              <ci>n</ci>
                              <cn>0</cn>
                           </apply>
                           <apply>
                              <csymbol cd="set1">in</csymbol>
                              <ci>n</ci>
                              <csymbol cd="setname1">Z</csymbol>
                           </apply>
                        </apply>
                     </bind>
                  </apply>
               </apply>
               <bind>
                  <csymbol cd="quant1">exists</csymbol>
                  <bvar>
                     <ci>x</ci>
                  </bvar>
                  <bvar>
                     <ci>y</ci>
                  </bvar>
                  <bvar>
                     <ci>z</ci>
                  </bvar>
                  <apply>
                     <csymbol cd="logic1">and</csymbol>
                     <apply>
                        <csymbol cd="set1">in</csymbol>
                        <ci>x</ci>
                        <ci>y</ci>
                        <ci>z</ci>
                        <apply>
                           <csymbol cd="set1">suchthat</csymbol>
                           <ci>R</ci>
                           <bind>
                              <csymbol cd="fns1">lambda</csymbol>
                              <bvar>
                                 <ci>x</ci>
                              </bvar>
                              <bvar>
                                 <ci>y</ci>
                              </bvar>
                              <bvar>
                                 <ci>z</ci>
                              </bvar>
                              <apply>
                                 <csymbol cd="logic1">and</csymbol>
                                 <apply>
                                    <csymbol cd="set1">in</csymbol>
                                    <ci>x</ci>
                                    <csymbol cd="setname1">Z</csymbol>
                                 </apply>
                                 <apply>
                                    <csymbol cd="set1">in</csymbol>
                                    <ci>y</ci>
                                    <csymbol cd="setname1">Z</csymbol>
                                 </apply>
                                 <apply>
                                    <csymbol cd="set1">in</csymbol>
                                    <ci>z</ci>
                                    <csymbol cd="setname1">Z</csymbol>
                                 </apply>
                              </apply>
                           </bind>
                        </apply>
                     </apply>
                     <apply>
                        <csymbol cd="relation1">eq</csymbol>
                        <apply>
                           <csymbol cd="arith1">plus</csymbol>
                           <apply>
                              <csymbol cd="arith1">power</csymbol>
                              <ci>x</ci>
                              <ci>n</ci>
                           </apply>
                           <apply>
                              <csymbol cd="arith1">power</csymbol>
                              <ci>y</ci>
                              <ci>n</ci>
                           </apply>
                        </apply>
                        <apply>
                           <csymbol cd="arith1">power</csymbol>
                           <ci>z</ci>
                           <ci>n</ci>
                        </apply>
                     </apply>
                  </apply>
               </bind>
            </apply>
         </bind>
      </math>