let K be Ring; :: thesis: for V being LeftMod of K
for W1, W2 being Subspace of V holds
( W1 c= W2 iff for a being Vector of V st a in W1 holds
a in W2 )
let V be LeftMod of K; :: thesis: for W1, W2 being Subspace of V holds
( W1 c= W2 iff for a being Vector of V st a in W1 holds
a in W2 )
let W1, W2 be Subspace of V; :: thesis: ( W1 c= W2 iff for a being Vector of V st a in W1 holds
a in W2 )
( W1 c= W2 iff W1 is Subspace of W2 ) by Def7;
hence ( W1 c= W2 iff for a being Vector of V st a in W1 holds
a in W2 ) by VECTSP_4:16, VECTSP_4:36; :: thesis: verum