• PhysicalConstants
    constant vacuum_dielectric_permitivity Show Notations
    LanguagesArgumentsRendering
    0ε_0
    constant elementary_charge Show Notations
    LanguagesArgumentsRendering
    0q
    constant Boltzmann_constant Show Notations
    LanguagesArgumentsRendering
    0k_B
  • Base
    includes PhysicalConstants
    includes LFSigma
    constant exp
    constant der Show Notations
    LanguagesArgumentsRendering
    2b'a
    constant Real_vec_space2 Show Notations
    LanguagesArgumentsRendering
    0ℝ2
    ℝ×ℝhttp://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Producthttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbershttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbers
    constant Real_vec_space3 Show Notations
    LanguagesArgumentsRendering
    0ℝ3
    ℝ×ℝ×ℝhttp://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Producthttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbershttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbershttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbers
    constant comp1[v:ℝ3](πlv)http://cds.omdoc.org/urtheories?LambdaPi?lambdavhttp://mathhub.info/MitM/Models?Base?Real_vec_space3http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projlv
    constant comp2[v:ℝ3](πl(πrv))http://cds.omdoc.org/urtheories?LambdaPi?lambdavhttp://mathhub.info/MitM/Models?Base?Real_vec_space3http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projlhttp://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projrv
    constant comp3[v:ℝ3](πr(πrv))http://cds.omdoc.org/urtheories?LambdaPi?lambdavhttp://mathhub.info/MitM/Models?Base?Real_vec_space3http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projrhttp://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projrv
    constant pred_as_sub2 Show Notations
    LanguagesArgumentsRendering
    1pred2a
    [P:ℝ2→bool]⟨ℝ2|([z:ℝ2](ded(Pz)))⟩http://cds.omdoc.org/urtheories?LambdaPi?lambdaPhttp://cds.omdoc.org/urtheories?LambdaPi?arrowhttp://mathhub.info/MitM/Models?Base?Real_vec_space2http://mathhub.info/MitM/Foundation?Logic?boolhttp://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtphttp://mathhub.info/MitM/Models?Base?Real_vec_space2http://cds.omdoc.org/urtheories?LambdaPi?lambdazhttp://mathhub.info/MitM/Models?Base?Real_vec_space2http://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Foundation?Logic?dedhttp://cds.omdoc.org/urtheories?LambdaPi?applyPz
    constant pred_as_sub3 Show Notations
    LanguagesArgumentsRendering
    1pred3a
    [P:ℝ3→bool]⟨ℝ3|([z:ℝ3](ded(Pz)))⟩http://cds.omdoc.org/urtheories?LambdaPi?lambdaPhttp://cds.omdoc.org/urtheories?LambdaPi?arrowhttp://mathhub.info/MitM/Models?Base?Real_vec_space3http://mathhub.info/MitM/Foundation?Logic?boolhttp://gl.mathhub.info/MMT/LFX/Subtyping?PredSubSymbols?predsubtphttp://mathhub.info/MitM/Models?Base?Real_vec_space3http://cds.omdoc.org/urtheories?LambdaPi?lambdazhttp://mathhub.info/MitM/Models?Base?Real_vec_space3http://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Foundation?Logic?dedhttp://cds.omdoc.org/urtheories?LambdaPi?applyPz
    constant lift_type_one_to_three Show Notations
    LanguagesArgumentsRendering
    1t1↑a
    [P:ℝ→bool]([v:ℝ3](and(and(P(comp1v))(eqℝ(comp2v)0))(eqℝ(comp3v)0)))http://cds.omdoc.org/urtheories?LambdaPi?lambdaPhttp://cds.omdoc.org/urtheories?LambdaPi?arrowhttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbershttp://mathhub.info/MitM/Foundation?Logic?boolhttp://cds.omdoc.org/urtheories?LambdaPi?lambdavhttp://mathhub.info/MitM/Models?Base?Real_vec_space3http://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Foundation?Logic?andhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Foundation?Logic?andhttp://cds.omdoc.org/urtheories?LambdaPi?applyPhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models?Base?comp1vhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Foundation?Logic?eqhttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbershttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models?Base?comp2v0http://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Foundation?Logic?eqhttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbershttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models?Base?comp3v0
    constant lift_type_two_to_three Show Notations
    LanguagesArgumentsRendering
    1t2↑a
    [P:ℝ2→bool]([v:ℝ3](and(P⟨(comp1v),(comp2v)⟩)(eqℝ(comp3v)0)))http://cds.omdoc.org/urtheories?LambdaPi?lambdaPhttp://cds.omdoc.org/urtheories?LambdaPi?arrowhttp://mathhub.info/MitM/Models?Base?Real_vec_space2http://mathhub.info/MitM/Foundation?Logic?boolhttp://cds.omdoc.org/urtheories?LambdaPi?lambdavhttp://mathhub.info/MitM/Models?Base?Real_vec_space3http://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Foundation?Logic?andhttp://cds.omdoc.org/urtheories?LambdaPi?applyPhttp://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuplehttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models?Base?comp1vhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models?Base?comp2vhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Foundation?Logic?eqhttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbershttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models?Base?comp3v0
    constant lift_function_one_to_three Show Notations
    LanguagesArgumentsRendering
    2f1↑ab
    constant lift_function_two_to_three Show Notations
    LanguagesArgumentsRendering
    2f2↑ab