let G be non empty addGroup-like addMagma ; :: thesis: for H being Subgroup of G st G is finite holds
H is finite
let H be Subgroup of G; :: thesis: ( G is finite implies H is finite )
assume A1: G is finite ; :: thesis: H is finite
the carrier of H c= the carrier of G by DefA5;
hence the carrier of H is finite by A1; :: according to STRUCT_0:def 11 :: thesis: verum