let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF

for W1, W2 being strict Subspace of V st the carrier of W1 = the carrier of W2 holds

W1 = W2

let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for W1, W2 being strict Subspace of V st the carrier of W1 = the carrier of W2 holds

W1 = W2

let W1, W2 be strict Subspace of V; :: thesis: ( the carrier of W1 = the carrier of W2 implies W1 = W2 )

assume the carrier of W1 = the carrier of W2 ; :: thesis: W1 = W2

then ( W1 is Subspace of W2 & W2 is Subspace of W1 ) by Th27;

hence W1 = W2 by Th25; :: thesis: verum

for W1, W2 being strict Subspace of V st the carrier of W1 = the carrier of W2 holds

W1 = W2

let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for W1, W2 being strict Subspace of V st the carrier of W1 = the carrier of W2 holds

W1 = W2

let W1, W2 be strict Subspace of V; :: thesis: ( the carrier of W1 = the carrier of W2 implies W1 = W2 )

assume the carrier of W1 = the carrier of W2 ; :: thesis: W1 = W2

then ( W1 is Subspace of W2 & W2 is Subspace of W1 ) by Th27;

hence W1 = W2 by Th25; :: thesis: verum