:: JORDAN10 semantic presentation
theorem Th1: :: JORDAN10:1
for b
1, b
2, b
3, b
4 being
Natfor b
5 being
connected compact non
horizontal non
vertical Subset of
(TOP-REAL 2) holds
not ( 1
<= b
1 & b
1 + 1
<= len (Cage b5,b2) &
[b3,b4] in Indices (Gauge b5,b2) &
[b3,(b4 + 1)] in Indices (Gauge b5,b2) &
(Cage b5,b2) /. b
1 = (Gauge b5,b2) * b
3,b
4 &
(Cage b5,b2) /. (b1 + 1) = (Gauge b5,b2) * b
3,
(b4 + 1) & not b
3 < len (Gauge b5,b2) )
theorem Th2: :: JORDAN10:2
for b
1, b
2, b
3, b
4 being
Natfor b
5 being
connected compact non
horizontal non
vertical Subset of
(TOP-REAL 2) holds
not ( 1
<= b
1 & b
1 + 1
<= len (Cage b5,b2) &
[b3,b4] in Indices (Gauge b5,b2) &
[b3,(b4 + 1)] in Indices (Gauge b5,b2) &
(Cage b5,b2) /. b
1 = (Gauge b5,b2) * b
3,
(b4 + 1) &
(Cage b5,b2) /. (b1 + 1) = (Gauge b5,b2) * b
3,b
4 & not b
3 > 1 )
theorem Th3: :: JORDAN10:3
for b
1, b
2, b
3, b
4 being
Natfor b
5 being
connected compact non
horizontal non
vertical Subset of
(TOP-REAL 2) holds
not ( 1
<= b
1 & b
1 + 1
<= len (Cage b5,b2) &
[b3,b4] in Indices (Gauge b5,b2) &
[(b3 + 1),b4] in Indices (Gauge b5,b2) &
(Cage b5,b2) /. b
1 = (Gauge b5,b2) * b
3,b
4 &
(Cage b5,b2) /. (b1 + 1) = (Gauge b5,b2) * (b3 + 1),b
4 & not b
4 > 1 )
theorem Th4: :: JORDAN10:4
for b
1, b
2, b
3, b
4 being
Natfor b
5 being
connected compact non
horizontal non
vertical Subset of
(TOP-REAL 2) holds
not ( 1
<= b
1 & b
1 + 1
<= len (Cage b5,b2) &
[b3,b4] in Indices (Gauge b5,b2) &
[(b3 + 1),b4] in Indices (Gauge b5,b2) &
(Cage b5,b2) /. b
1 = (Gauge b5,b2) * (b3 + 1),b
4 &
(Cage b5,b2) /. (b1 + 1) = (Gauge b5,b2) * b
3,b
4 & not b
4 < width (Gauge b5,b2) )
theorem Th5: :: JORDAN10:5
theorem Th6: :: JORDAN10:6
theorem Th7: :: JORDAN10:7
theorem Th8: :: JORDAN10:8
theorem Th9: :: JORDAN10:9
theorem Th10: :: JORDAN10:10
theorem Th11: :: JORDAN10:11
theorem Th12: :: JORDAN10:12
theorem Th13: :: JORDAN10:13
:: deftheorem Def1 defines UBD-Family JORDAN10:def 1 :
:: deftheorem Def2 defines BDD-Family JORDAN10:def 2 :
theorem Th14: :: JORDAN10:14
theorem Th15: :: JORDAN10:15
theorem Th16: :: JORDAN10:16
theorem Th17: :: JORDAN10:17
theorem Th18: :: JORDAN10:18
theorem Th19: :: JORDAN10:19
theorem Th20: :: JORDAN10:20
theorem Th21: :: JORDAN10:21