:: PRGCOR_2 semantic presentation
theorem Th1: :: PRGCOR_2:1
for b
1, b
2 being
Nat holds
( b
1 in b
2 iff b
1 < b
2 )
theorem Th2: :: PRGCOR_2:2
:: deftheorem Def1 defines FS2XFS PRGCOR_2:def 1 :
:: deftheorem Def2 defines XFS2FS PRGCOR_2:def 2 :
theorem Th3: :: PRGCOR_2:3
theorem Th4: :: PRGCOR_2:4
:: deftheorem Def3 defines FS2XFS* PRGCOR_2:def 3 :
:: deftheorem Def4 defines XFS2FS* PRGCOR_2:def 4 :
theorem Th5: :: PRGCOR_2:5
:: deftheorem Def5 defines is_an_xrep_of PRGCOR_2:def 5 :
theorem Th6: :: PRGCOR_2:6
:: deftheorem Def6 defines IFLGT PRGCOR_2:def 6 :
for b
1, b
2, b
3, b
4, b
5 being
set holds
( ( b
1 in b
2 implies
IFLGT b
1,b
2,b
3,b
4,b
5 = b
3 ) & ( b
1 = b
2 implies
IFLGT b
1,b
2,b
3,b
4,b
5 = b
4 ) & ( not b
1 in b
2 & not b
1 = b
2 implies
IFLGT b
1,b
2,b
3,b
4,b
5 = b
5 ) );
theorem Th7: :: PRGCOR_2:7
:: deftheorem Def7 defines inner_prd_prg PRGCOR_2:def 7 :
theorem Th8: :: PRGCOR_2:8
theorem Th9: :: PRGCOR_2:9
theorem Th10: :: PRGCOR_2:10
:: deftheorem Def8 defines scalar_prd_prg PRGCOR_2:def 8 :
theorem Th11: :: PRGCOR_2:11
:: deftheorem Def9 defines vector_minus_prg PRGCOR_2:def 9 :
theorem Th12: :: PRGCOR_2:12
:: deftheorem Def10 defines vector_add_prg PRGCOR_2:def 10 :
theorem Th13: :: PRGCOR_2:13
:: deftheorem Def11 defines vector_sub_prg PRGCOR_2:def 11 :
theorem Th14: :: PRGCOR_2:14