begin
theorem Th1:
theorem
theorem Th3:
theorem Th4:
theorem Th5:
begin
theorem Th6:
theorem Th7:
theorem
theorem Th9:
theorem Th10:
theorem Th11:
theorem Th12:
theorem Th13:
begin
theorem Th14:
theorem
theorem
theorem
theorem
theorem
begin
theorem Th20:
theorem Th21:
theorem Th22:
theorem Th23:
theorem Th24:
theorem Th25:
theorem Th26:
theorem Th27:
theorem Th28:
theorem Th29:
theorem
theorem Th31:
begin
theorem Th32:
theorem Th33:
theorem Th34:
theorem Th35:
theorem Th36:
theorem
begin
definition
let n be
Element of
NAT ;
let A,
B be
Subset of ;
func dist_min A,
B -> Real means :
Def1:
ex
A',
B' being
Subset of st
(
A = A' &
B = B' &
it = min_dist_min A',
B' );
existence
ex b1 being Real ex A', B' being Subset of st
( A = A' & B = B' & b1 = min_dist_min A',B' )
uniqueness
for b1, b2 being Real st ex A', B' being Subset of st
( A = A' & B = B' & b1 = min_dist_min A',B' ) & ex A', B' being Subset of st
( A = A' & B = B' & b2 = min_dist_min A',B' ) holds
b1 = b2
;
end;
:: deftheorem Def1 defines dist_min JORDAN1K:def 1 :
theorem Th38:
theorem Th39:
theorem Th40:
theorem Th41:
theorem Th42:
theorem Th43:
:: deftheorem defines dist JORDAN1K:def 2 :
theorem
theorem
theorem Th46:
theorem
theorem
theorem
theorem Th50:
theorem