begin
theorem Th1:
theorem Th2:
theorem Th3:
Lm1:
for X, x being set st x in X holds
(X \ {x}) \/ {x} = X
theorem
canceled;
theorem Th5:
theorem Th6:
theorem Th7:
theorem Th8:
theorem Th9:
theorem Th10:
theorem Th11:
theorem Th12:
theorem Th13:
theorem Th14:
theorem Th15:
theorem Th16:
theorem Th17:
theorem Th18:
theorem Th19:
theorem Th20:
theorem Th21:
begin
theorem Th22:
theorem Th23:
begin
:: deftheorem Def1 defines finite-dimensional RLVECT_5:def 1 :
theorem Th24:
theorem
theorem Th26:
theorem Th27:
theorem Th28:
begin
:: deftheorem RLVECT_5:def 2 :
canceled;
:: deftheorem Def3 defines dim RLVECT_5:def 3 :
theorem Th29:
theorem Th30:
theorem Th31:
theorem
theorem Th33:
theorem
theorem
theorem Th36:
theorem
theorem
Lm2:
for n being Element of NAT
for V being finite-dimensional RealLinearSpace st n <= dim V holds
ex W being strict Subspace of V st dim W = n
theorem
:: deftheorem Def4 defines Subspaces_of RLVECT_5:def 4 :
theorem
theorem
theorem