:: MEASURE2 semantic presentation
theorem Th1: :: MEASURE2:1
:: deftheorem Def1 defines N_Measure_fam MEASURE2:def 1 :
theorem Th2: :: MEASURE2:2
canceled;
theorem Th3: :: MEASURE2:3
theorem Th4: :: MEASURE2:4
theorem Th5: :: MEASURE2:5
theorem Th6: :: MEASURE2:6
theorem Th7: :: MEASURE2:7
theorem Th8: :: MEASURE2:8
theorem Th9: :: MEASURE2:9
theorem Th10: :: MEASURE2:10
theorem Th11: :: MEASURE2:11
theorem Th12: :: MEASURE2:12
canceled;
theorem Th13: :: MEASURE2:13
theorem Th14: :: MEASURE2:14
theorem Th15: :: MEASURE2:15
theorem Th16: :: MEASURE2:16
theorem Th17: :: MEASURE2:17
theorem Th18: :: MEASURE2:18
:: deftheorem Def2 defines non-decreasing MEASURE2:def 2 :
:: deftheorem Def3 defines non-increasing MEASURE2:def 3 :
theorem Th19: :: MEASURE2:19
canceled;
theorem Th20: :: MEASURE2:20
canceled;
theorem Th21: :: MEASURE2:21
theorem Th22: :: MEASURE2:22
for b
1 being
Function holds
( ( for b
2 being
Element of
NAT holds b
1 . b
2 c= b
1 . (b2 + 1) ) implies for b
2, b
3 being
Nat holds
( b
3 <= b
2 implies b
1 . b
3 c= b
1 . b
2 ) )
theorem Th23: :: MEASURE2:23
for b
1, b
2 being
Function holds
( b
2 . 0
= b
1 . 0 & ( for b
3 being
Element of
NAT holds
( b
2 . (b3 + 1) = (b1 . (b3 + 1)) \ (b1 . b3) & b
1 . b
3 c= b
1 . (b3 + 1) ) ) implies for b
3, b
4 being
Nat holds
( b
3 < b
4 implies b
2 . b
3 misses b
2 . b
4 ) )
theorem Th24: :: MEASURE2:24
theorem Th25: :: MEASURE2:25
theorem Th26: :: MEASURE2:26
theorem Th27: :: MEASURE2:27