begin
theorem
canceled;
theorem
canceled;
theorem Th3:
theorem Th4:
theorem Th5:
begin
theorem Th6:
theorem Th7:
theorem Th8:
theorem Th9:
begin
theorem Th10:
theorem Th11:
theorem Th12:
begin
theorem Th13:
theorem Th14:
theorem Th15:
theorem Th16:
theorem Th17:
theorem Th18:
theorem
theorem
theorem
theorem
theorem Th23:
theorem Th24:
theorem Th25:
theorem Th26:
theorem Th27:
theorem Th28:
theorem
theorem Th30:
theorem Th31:
theorem Th32:
begin
theorem Th33:
theorem Th34:
theorem Th35:
theorem Th36:
begin
:: deftheorem defines SpStSeq SPRECT_1:def 1 :
theorem Th37:
theorem Th38:
theorem Th39:
theorem Th40:
theorem
theorem Th42:
theorem Th43:
theorem Th44:
theorem
canceled;
theorem Th46:
theorem Th47:
theorem Th48:
theorem Th49:
theorem Th50:
theorem Th51:
theorem Th52:
theorem Th53:
theorem Th54:
theorem Th55:
theorem Th56:
theorem Th57:
theorem
canceled;
theorem Th59:
for
r1,
r2,
t being
Real st
r1 <= r2 holds
(
t in [.r1,r2.] iff ex
s1 being
Real st
(
0 <= s1 &
s1 <= 1 &
t = (s1 * r1) + ((1 - s1) * r2) ) )
theorem Th60:
theorem Th61:
theorem Th62:
theorem Th63:
theorem Th64:
theorem Th65:
theorem Th66:
theorem Th67:
theorem Th68:
theorem Th69:
theorem Th70:
theorem Th71:
theorem Th72:
theorem Th73:
theorem Th74:
theorem Th75:
theorem Th76:
theorem Th77:
theorem Th78:
theorem Th79:
theorem Th80:
theorem Th81:
theorem Th82:
theorem Th83:
theorem Th84:
theorem Th85:
theorem Th86:
theorem Th87:
theorem Th88:
theorem Th89:
begin
:: deftheorem Def2 defines rectangular SPRECT_1:def 2 :
theorem
theorem
theorem
theorem
theorem
begin
theorem Th95:
for
r1,
r2,
s1,
s2 being
Real st
r1 < r2 &
s1 < s2 holds
[.r1,r2,s1,s2.] is
Jordan
:: deftheorem Def3 defines Jordan SPRECT_1:def 3 :
theorem Th96:
theorem