let R be domRing; :: thesis: for V being strict LeftMod of R
for A being Subset of V st 0. R <> 1. R & A = the carrier of V holds
Lin A = V
let V be strict LeftMod of R; :: thesis: for A being Subset of V st 0. R <> 1. R & A = the carrier of V holds
Lin A = V
let A be Subset of V; :: thesis: ( 0. R <> 1. R & A = the carrier of V implies Lin A = V )
assume A1: 0. R <> 1. R ; :: thesis: ( not A = the carrier of V or Lin A = V )
A2: (Omega). V = V ;
assume A = the carrier of V ; :: thesis: Lin A = V
hence Lin A = V by A1, A2, Th13; :: thesis: verum