let V be RealLinearSpace; :: thesis: for x being object
for W1, W2 being Subspace of V st x in W1 & W1 is Subspace of W2 holds
x in W2
let x be object ; :: thesis: for W1, W2 being Subspace of V st x in W1 & W1 is Subspace of W2 holds
x in W2
let W1, W2 be Subspace of V; :: thesis: ( x in W1 & W1 is Subspace of W2 implies x in W2 )
assume ( x in W1 & W1 is Subspace of W2 ) ; :: thesis: x in W2
then ( x in the carrier of W1 & the carrier of W1 c= the carrier of W2 ) by Def2;
hence x in W2 ; :: thesis: verum