:: VECTSP_9 semantic presentation
theorem Th1: :: VECTSP_9:1
canceled;
theorem Th2: :: VECTSP_9:2
canceled;
theorem Th3: :: VECTSP_9:3
canceled;
theorem Th4: :: VECTSP_9:4
canceled;
Lemma1:
for b1, b2 being set holds
( b2 in b1 implies (b1 \ {b2}) \/ {b2} = b1 )
theorem Th5: :: VECTSP_9:5
theorem Th6: :: VECTSP_9:6
theorem Th7: :: VECTSP_9:7
theorem Th8: :: VECTSP_9:8
theorem Th9: :: VECTSP_9:9
theorem Th10: :: VECTSP_9:10
theorem Th11: :: VECTSP_9:11
theorem Th12: :: VECTSP_9:12
theorem Th13: :: VECTSP_9:13
theorem Th14: :: VECTSP_9:14
theorem Th15: :: VECTSP_9:15
theorem Th16: :: VECTSP_9:16
theorem Th17: :: VECTSP_9:17
theorem Th18: :: VECTSP_9:18
theorem Th19: :: VECTSP_9:19
theorem Th20: :: VECTSP_9:20
theorem Th21: :: VECTSP_9:21
theorem Th22: :: VECTSP_9:22
theorem Th23: :: VECTSP_9:23
:: deftheorem Def1 defines finite-dimensional VECTSP_9:def 1 :
theorem Th24: :: VECTSP_9:24
theorem Th25: :: VECTSP_9:25
theorem Th26: :: VECTSP_9:26
theorem Th27: :: VECTSP_9:27
theorem Th28: :: VECTSP_9:28
:: deftheorem Def2 defines dim VECTSP_9:def 2 :
theorem Th29: :: VECTSP_9:29
theorem Th30: :: VECTSP_9:30
theorem Th31: :: VECTSP_9:31
theorem Th32: :: VECTSP_9:32
theorem Th33: :: VECTSP_9:33
theorem Th34: :: VECTSP_9:34
theorem Th35: :: VECTSP_9:35
theorem Th36: :: VECTSP_9:36
theorem Th37: :: VECTSP_9:37
theorem Th38: :: VECTSP_9:38
Lemma32:
for b1 being Field
for b2 being Nat
for b3 being finite-dimensional VectSp of b1 holds
not ( b2 <= dim b3 & ( for b4 being strict Subspace of b3 holds
not dim b4 = b2 ) )
theorem Th39: :: VECTSP_9:39
:: deftheorem Def3 defines Subspaces_of VECTSP_9:def 3 :
theorem Th40: :: VECTSP_9:40
theorem Th41: :: VECTSP_9:41
theorem Th42: :: VECTSP_9:42