:: URYSOHN2 semantic presentation
theorem Th1: :: URYSOHN2:1
theorem Th2: :: URYSOHN2:2
theorem Th3: :: URYSOHN2:3
theorem Th4: :: URYSOHN2:4
theorem Th5: :: URYSOHN2:5
theorem Th6: :: URYSOHN2:6
theorem Th7: :: URYSOHN2:7
theorem Th8: :: URYSOHN2:8
theorem Th9: :: URYSOHN2:9
theorem Th10: :: URYSOHN2:10
theorem Th11: :: URYSOHN2:11
theorem Th12: :: URYSOHN2:12
theorem Th13: :: URYSOHN2:13
theorem Th14: :: URYSOHN2:14
theorem Th15: :: URYSOHN2:15
theorem Th16: :: URYSOHN2:16
theorem Th17: :: URYSOHN2:17
theorem Th18: :: URYSOHN2:18
theorem Th19: :: URYSOHN2:19
theorem Th20: :: URYSOHN2:20
theorem Th21: :: URYSOHN2:21
canceled;
theorem Th22: :: URYSOHN2:22
canceled;
theorem Th23: :: URYSOHN2:23
for b
1 being
Real holds
not ( 0
< b
1 & ( for b
2 being
Nat holds not 1
< (2 |^ b2) * b
1 ) )
theorem Th24: :: URYSOHN2:24
for b
1, b
2 being
Real holds
not ( 0
<= b
1 & 1
< b
2 - b
1 & ( for b
3 being
Nat holds
not ( b
1 < b
3 & b
3 < b
2 ) ) )
theorem Th25: :: URYSOHN2:25
canceled;
theorem Th26: :: URYSOHN2:26
canceled;
theorem Th27: :: URYSOHN2:27
theorem Th28: :: URYSOHN2:28
for b
1, b
2 being
Real holds
not ( b
1 < b
2 & 0
<= b
1 & b
2 <= 1 & ( for b
3 being
Real holds
not ( b
3 in DYADIC & b
1 < b
3 & b
3 < b
2 ) ) )
theorem Th29: :: URYSOHN2:29
for b
1, b
2 being
Real holds
not ( b
1 < b
2 & ( for b
3 being
Real holds
not ( b
3 in DOM & b
1 < b
3 & b
3 < b
2 ) ) )
theorem Th30: :: URYSOHN2:30
theorem Th31: :: URYSOHN2:31
theorem Th32: :: URYSOHN2:32
theorem Th33: :: URYSOHN2:33
theorem Th34: :: URYSOHN2:34
for b
1, b
2, b
3, b
4 being
Real holds
not ( b
1 < b
3 & b
3 < b
2 & b
1 < b
4 & b
4 < b
2 & not
abs (b4 - b3) < b
2 - b
1 )
theorem Th35: :: URYSOHN2:35