:: YELLOW16 semantic presentation
theorem :: YELLOW16:1
theorem :: YELLOW16:2
theorem :: YELLOW16:3
theorem :: YELLOW16:4
theorem Th5: :: YELLOW16:5
theorem Th6: :: YELLOW16:6
Lm1:
for S, T being non empty 1-sorted
for f being Function of T,S
for g being Function of S,T st f * g = id S holds
rng f = the carrier of S
by FUNCT_2:29;
theorem :: YELLOW16:7
canceled;
theorem :: YELLOW16:8
canceled;
theorem Th9: :: YELLOW16:9
:: deftheorem Def1 defines is_a_retraction_of YELLOW16:def 1 :
:: deftheorem Def2 defines is_an_UPS_retraction_of YELLOW16:def 2 :
:: deftheorem Def3 defines is_a_retract_of YELLOW16:def 3 :
:: deftheorem Def4 defines is_an_UPS_retract_of YELLOW16:def 4 :
theorem Th10: :: YELLOW16:10
theorem Th11: :: YELLOW16:11
theorem Th12: :: YELLOW16:12
theorem Th13: :: YELLOW16:13
theorem Th14: :: YELLOW16:14
theorem Th15: :: YELLOW16:15
theorem Th16: :: YELLOW16:16
theorem Th17: :: YELLOW16:17
theorem Th18: :: YELLOW16:18
theorem :: YELLOW16:19
theorem Th20: :: YELLOW16:20
theorem Th21: :: YELLOW16:21
theorem Th22: :: YELLOW16:22
theorem Th23: :: YELLOW16:23
theorem Th24: :: YELLOW16:24
theorem :: YELLOW16:25
theorem :: YELLOW16:26
theorem :: YELLOW16:27
theorem Th28: :: YELLOW16:28
theorem :: YELLOW16:29
theorem :: YELLOW16:30
:: deftheorem Def5 defines Poset-yielding YELLOW16:def 5 :
theorem Th31: :: YELLOW16:31
theorem Th32: :: YELLOW16:32
theorem Th33: :: YELLOW16:33
theorem Th34: :: YELLOW16:34
theorem Th35: :: YELLOW16:35
theorem Th36: :: YELLOW16:36
theorem Th37: :: YELLOW16:37
theorem Th38: :: YELLOW16:38
theorem Th39: :: YELLOW16:39
theorem :: YELLOW16:40
theorem Th41: :: YELLOW16:41
:: deftheorem Def6 defines inherits_sup_of YELLOW16:def 6 :
:: deftheorem Def7 defines inherits_inf_of YELLOW16:def 7 :
theorem Th42: :: YELLOW16:42
theorem :: YELLOW16:43
theorem :: YELLOW16:44
theorem Th45: :: YELLOW16:45
theorem Th46: :: YELLOW16:46
theorem :: YELLOW16:47
theorem Th48: :: YELLOW16:48
theorem :: YELLOW16:49
theorem :: YELLOW16:50
theorem :: YELLOW16:51
theorem :: YELLOW16:52
theorem :: YELLOW16:53
theorem Th54: :: YELLOW16:54
theorem Th55: :: YELLOW16:55
theorem Th56: :: YELLOW16:56
theorem Th57: :: YELLOW16:57
theorem Th58: :: YELLOW16:58
theorem :: YELLOW16:59