take
V
; :: thesis: ( the carrier of V c= the carrier of V & the addF of V = the addF of V || the carrier of V & the multF of V = the multF of V || the carrier of V & the Mult of V = the Mult of V | [:COMPLEX, the carrier of V:] & 1. V = 1. V & 0. V = 0. V )

thus ( the carrier of V c= the carrier of V & the addF of V = the addF of V || the carrier of V & the multF of V = the multF of V || the carrier of V & the Mult of V = the Mult of V | [:COMPLEX, the carrier of V:] & 1. V = 1. V & 0. V = 0. V ) by RELSET_1:19; :: thesis: verum

thus ( the carrier of V c= the carrier of V & the addF of V = the addF of V || the carrier of V & the multF of V = the multF of V || the carrier of V & the Mult of V = the Mult of V | [:COMPLEX, the carrier of V:] & 1. V = 1. V & 0. V = 0. V ) by RELSET_1:19; :: thesis: verum