:: NCFCONT2 semantic presentation
:: deftheorem Def1 defines is_uniformly_continuous_on NCFCONT2:def 1 :
:: deftheorem Def2 defines is_uniformly_continuous_on NCFCONT2:def 2 :
:: deftheorem Def3 defines is_uniformly_continuous_on NCFCONT2:def 3 :
:: deftheorem Def4 defines is_uniformly_continuous_on NCFCONT2:def 4 :
:: deftheorem Def5 defines is_uniformly_continuous_on NCFCONT2:def 5 :
:: deftheorem Def6 defines is_uniformly_continuous_on NCFCONT2:def 6 :
theorem Th1: :: NCFCONT2:1
theorem Th2: :: NCFCONT2:2
theorem Th3: :: NCFCONT2:3
theorem Th4: :: NCFCONT2:4
theorem Th5: :: NCFCONT2:5
theorem Th6: :: NCFCONT2:6
theorem Th7: :: NCFCONT2:7
theorem Th8: :: NCFCONT2:8
theorem Th9: :: NCFCONT2:9
theorem Th10: :: NCFCONT2:10
theorem Th11: :: NCFCONT2:11
theorem Th12: :: NCFCONT2:12
theorem Th13: :: NCFCONT2:13
theorem Th14: :: NCFCONT2:14
theorem Th15: :: NCFCONT2:15
theorem Th16: :: NCFCONT2:16
theorem Th17: :: NCFCONT2:17
theorem Th18: :: NCFCONT2:18
theorem Th19: :: NCFCONT2:19
theorem Th20: :: NCFCONT2:20
theorem Th21: :: NCFCONT2:21
theorem Th22: :: NCFCONT2:22
theorem Th23: :: NCFCONT2:23
theorem Th24: :: NCFCONT2:24
theorem Th25: :: NCFCONT2:25
theorem Th26: :: NCFCONT2:26
theorem Th27: :: NCFCONT2:27
theorem Th28: :: NCFCONT2:28
theorem Th29: :: NCFCONT2:29
theorem Th30: :: NCFCONT2:30
theorem Th31: :: NCFCONT2:31
theorem Th32: :: NCFCONT2:32
theorem Th33: :: NCFCONT2:33
theorem Th34: :: NCFCONT2:34
theorem Th35: :: NCFCONT2:35
theorem Th36: :: NCFCONT2:36
theorem Th37: :: NCFCONT2:37
:: deftheorem Def7 defines contraction NCFCONT2:def 7 :
theorem Th38: :: NCFCONT2:38
theorem Th39: :: NCFCONT2:39
Lemma126:
for X being ComplexNormSpace
for x, y, z being Point of X
for e being Real st e > 0 & ||.(x - z).|| < e / 2 & ||.(z - y).|| < e / 2 holds
||.(x - y).|| < e
Lemma128:
for X being ComplexNormSpace
for x, y, z being Point of X
for e being Real st e > 0 & ||.(x - z).|| < e / 2 & ||.(y - z).|| < e / 2 holds
||.(x - y).|| < e
Lemma129:
for X being ComplexNormSpace
for x being Point of X st ( for e being Real st e > 0 holds
||.x.|| < e ) holds
x = 0. X
Lemma130:
for X being ComplexNormSpace
for x, y being Point of X st ( for e being Real st e > 0 holds
||.(x - y).|| < e ) holds
x = y
Lemma131:
for K, L, e being real number st 0 < K & K < 1 & 0 < e holds
ex n being Element of NAT st abs (L * (K to_power n)) < e
by NFCONT_2:16;
theorem Th40: :: NCFCONT2:40
theorem Th41: :: NCFCONT2:41