:: RFINSEQ2 semantic presentation
:: deftheorem Def1 defines max_p RFINSEQ2:def 1 :
:: deftheorem Def2 defines min_p RFINSEQ2:def 2 :
:: deftheorem Def3 defines max RFINSEQ2:def 3 :
:: deftheorem Def4 defines min RFINSEQ2:def 4 :
theorem Th1: :: RFINSEQ2:1
theorem Th2: :: RFINSEQ2:2
theorem Th3: :: RFINSEQ2:3
theorem Th4: :: RFINSEQ2:4
theorem Th5: :: RFINSEQ2:5
theorem Th6: :: RFINSEQ2:6
theorem Th7: :: RFINSEQ2:7
theorem Th8: :: RFINSEQ2:8
theorem Th9: :: RFINSEQ2:9
theorem Th10: :: RFINSEQ2:10
theorem Th11: :: RFINSEQ2:11
theorem Th12: :: RFINSEQ2:12
theorem Th13: :: RFINSEQ2:13
Lemma81:
for f, g being FinSequence of REAL st f,g are_fiberwise_equipotent holds
max f <= max g
theorem Th14: :: RFINSEQ2:14
Lemma84:
for f, g being FinSequence of REAL st f,g are_fiberwise_equipotent holds
min f >= min g
theorem Th15: :: RFINSEQ2:15
:: deftheorem Def5 defines sort_d RFINSEQ2:def 5 :
theorem Th16: :: RFINSEQ2:16
theorem Th17: :: RFINSEQ2:17
Lemma92:
for f, g being non-decreasing 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 )
theorem Th18: :: RFINSEQ2:18
Lemma96:
for n being Element of NAT
for g1, g2 being non-decreasing FinSequence of REAL st n = len g1 & g1,g2 are_fiberwise_equipotent holds
g1 = g2
theorem Th19: :: RFINSEQ2:19
:: deftheorem Def6 defines sort_a RFINSEQ2:def 6 :
theorem Th20: :: RFINSEQ2:20
theorem Th21: :: RFINSEQ2:21
theorem Th22: :: RFINSEQ2:22
theorem Th23: :: RFINSEQ2:23
theorem Th24: :: RFINSEQ2:24
theorem Th25: :: RFINSEQ2:25
theorem Th26: :: RFINSEQ2:26
theorem Th27: :: RFINSEQ2:27
theorem Th28: :: RFINSEQ2:28
theorem Th29: :: RFINSEQ2:29
theorem Th30: :: RFINSEQ2:30
theorem Th31: :: RFINSEQ2:31
theorem Th32: :: RFINSEQ2:32