:: RFINSEQ semantic presentation
:: deftheorem Def1 defines are_fiberwise_equipotent RFINSEQ:def 1 :
Lemma30:
for F being Function
for x being set st not x in rng F holds
F " {x} = {}
theorem Th1: :: RFINSEQ:1
theorem Th2: :: RFINSEQ:2
theorem Th3: :: RFINSEQ:3
theorem Th4: :: RFINSEQ:4
theorem Th5: :: RFINSEQ:5
theorem Th6: :: RFINSEQ:6
theorem Th7: :: RFINSEQ:7
theorem Th8: :: RFINSEQ:8
canceled;
theorem Th9: :: RFINSEQ:9
theorem Th10: :: RFINSEQ:10
theorem Th11: :: RFINSEQ:11
theorem Th12: :: RFINSEQ:12
canceled;
theorem Th13: :: RFINSEQ:13
theorem Th14: :: RFINSEQ:14
theorem Th15: :: RFINSEQ:15
theorem Th16: :: RFINSEQ:16
theorem Th17: :: RFINSEQ:17
defpred S1[ Element of NAT ] means for X being finite set
for F being Function st card (dom (F | X)) = a1 holds
ex a being FinSequence st F | X,a are_fiberwise_equipotent ;
Lemma93:
S1[0]
Lemma95:
for n being Element of NAT st S1[n] holds
S1[n + 1]
theorem Th18: :: RFINSEQ:18
:: deftheorem Def2 defines /^ RFINSEQ:def 2 :
Lemma106:
for n being Element of NAT
for D being non empty set
for f being FinSequence of D st len f <= n holds
f | n = f
theorem Th19: :: RFINSEQ:19
theorem Th20: :: RFINSEQ:20
theorem Th21: :: RFINSEQ:21
theorem Th22: :: RFINSEQ:22
:: deftheorem Def3 defines MIM RFINSEQ:def 3 :
theorem Th23: :: RFINSEQ:23
theorem Th24: :: RFINSEQ:24
theorem Th25: :: RFINSEQ:25
theorem Th26: :: RFINSEQ:26
theorem Th27: :: RFINSEQ:27
theorem Th28: :: RFINSEQ:28
theorem Th29: :: RFINSEQ:29
theorem Th30: :: RFINSEQ:30
:: deftheorem Def4 defines non-increasing RFINSEQ:def 4 :
theorem Th31: :: RFINSEQ:31
theorem Th32: :: RFINSEQ:32
theorem Th33: :: RFINSEQ:33
theorem Th34: :: RFINSEQ:34
Lemma135:
for f, g being non-increasing FinSequence of REAL
for n being Element of NAT st len f = n + 1 & len f = len g & f,g are_fiberwise_equipotent holds
( f . (len f) = g . (len g) & f | n,g | n are_fiberwise_equipotent )
defpred S2[ Element of NAT ] means for R being FinSequence of REAL st a1 = len R holds
ex b being non-increasing FinSequence of REAL st R,b are_fiberwise_equipotent ;
Lemma137:
S2[0]
Lemma138:
for n being Element of NAT st S2[n] holds
S2[n + 1]
theorem Th35: :: RFINSEQ:35
Lemma163:
for n being Element of NAT
for g1, g2 being non-increasing FinSequence of REAL st n = len g1 & g1,g2 are_fiberwise_equipotent holds
g1 = g2
theorem Th36: :: RFINSEQ:36
theorem Th37: :: RFINSEQ:37
theorem Th38: :: RFINSEQ:38
theorem Th39: :: RFINSEQ:39