let H1, H2 be strict Subgroup of GroupHomography3 ; :: thesis: ( the carrier of H1 = EnsK-isometry & the carrier of H2 = EnsK-isometry implies H1 = H2 )
assume that
A44: the carrier of H1 = EnsK-isometry and
A45: the carrier of H2 = EnsK-isometry ; :: thesis: H1 = H2
for g being object holds
( g in H1 iff g in H2 ) by A44, A45;
hence H1 = H2 ; :: thesis: verum