:: WAYBEL32 semantic presentation
:: deftheorem Def1 defines upper WAYBEL32:def 1 :
:: deftheorem Def2 defines order_consistent WAYBEL32:def 2 :
theorem Th1: :: WAYBEL32:1
theorem Th2: :: WAYBEL32:2
theorem Th3: :: WAYBEL32:3
canceled;
theorem Th4: :: WAYBEL32:4
canceled;
theorem Th5: :: WAYBEL32:5
canceled;
theorem Th6: :: WAYBEL32:6
canceled;
theorem Th7: :: WAYBEL32:7
theorem Th8: :: WAYBEL32:8
theorem Th9: :: WAYBEL32:9
theorem Th10: :: WAYBEL32:10
theorem Th11: :: WAYBEL32:11
theorem Th12: :: WAYBEL32:12
theorem Th13: :: WAYBEL32:13
theorem Th14: :: WAYBEL32:14
theorem Th15: :: WAYBEL32:15
theorem Th16: :: WAYBEL32:16
theorem Th17: :: WAYBEL32:17
theorem Th18: :: WAYBEL32:18
theorem Th19: :: WAYBEL32:19
theorem Th20: :: WAYBEL32:20
theorem Th21: :: WAYBEL32:21
theorem Th22: :: WAYBEL32:22
theorem Th23: :: WAYBEL32:23
theorem Th24: :: WAYBEL32:24
theorem Th25: :: WAYBEL32:25
theorem Th26: :: WAYBEL32:26
theorem Th27: :: WAYBEL32:27
definition
let c
1 be non
empty 1-sorted ;
let c
2 be non
empty RelStr ;
let c
3 be
Function of the
carrier of c
2,the
carrier of c
1;
func c
2 *' c
3 -> non
empty strict NetStr of a
1 means :
Def3:
:: WAYBEL32:def 3
(
RelStr(# the
carrier of a
4,the
InternalRel of a
4 #)
= RelStr(# the
carrier of a
2,the
InternalRel of a
2 #) & the
mapping of a
4 = a
3 );
existence
ex b1 being non empty strict NetStr of c1 st
( RelStr(# the carrier of b1,the InternalRel of b1 #) = RelStr(# the carrier of c2,the InternalRel of c2 #) & the mapping of b1 = c3 )
uniqueness
for b1, b2 being non empty strict NetStr of c1 holds
( RelStr(# the carrier of b1,the InternalRel of b1 #) = RelStr(# the carrier of c2,the InternalRel of c2 #) & the mapping of b1 = c3 & RelStr(# the carrier of b2,the InternalRel of b2 #) = RelStr(# the carrier of c2,the InternalRel of c2 #) & the mapping of b2 = c3 implies b1 = b2 )
;
end;
:: deftheorem Def3 defines *' WAYBEL32:def 3 :
:: deftheorem Def4 defines inf_net WAYBEL32:def 4 :
theorem Th28: :: WAYBEL32:28
theorem Th29: :: WAYBEL32:29
theorem Th30: :: WAYBEL32:30
theorem Th31: :: WAYBEL32:31
theorem Th32: :: WAYBEL32:32
theorem Th33: :: WAYBEL32:33
theorem Th34: :: WAYBEL32:34