:: NAT_2 semantic presentation
theorem Th1: :: NAT_2:1
canceled;
theorem Th2: :: NAT_2:2
theorem Th3: :: NAT_2:3
canceled;
theorem Th4: :: NAT_2:4
theorem Th5: :: NAT_2:5
theorem Th6: :: NAT_2:6
for b
1 being
Nat holds b
1 div 1
= b
1
theorem Th7: :: NAT_2:7
theorem Th8: :: NAT_2:8
theorem Th9: :: NAT_2:9
theorem Th10: :: NAT_2:10
theorem Th11: :: NAT_2:11
theorem Th12: :: NAT_2:12
theorem Th13: :: NAT_2:13
theorem Th14: :: NAT_2:14
theorem Th15: :: NAT_2:15
theorem Th16: :: NAT_2:16
theorem Th17: :: NAT_2:17
theorem Th18: :: NAT_2:18
theorem Th19: :: NAT_2:19
theorem Th20: :: NAT_2:20
for b
1 being
Nat holds
( b
1 > 0 implies ( b
1 mod 2
= 0 iff
(b1 -' 1) mod 2
= 1 ) )
theorem Th21: :: NAT_2:21
theorem Th22: :: NAT_2:22
theorem Th23: :: NAT_2:23
theorem Th24: :: NAT_2:24
for b
1 being
Nat holds
( not b
1 is
even iff b
1 mod 2
= 1 )
theorem Th25: :: NAT_2:25
theorem Th26: :: NAT_2:26
for b
1, b
2, b
3 being
Nat holds
( b
1 <= b
2 implies b
1 div b
3 <= b
2 div b
3 )
theorem Th27: :: NAT_2:27
for b
1, b
2 being
Nat holds
( b
2 <= 2
* b
1 implies
(b2 + 1) div 2
<= b
1 )
theorem Th28: :: NAT_2:28
theorem Th29: :: NAT_2:29
:: deftheorem Def1 defines trivial NAT_2:def 1 :
theorem Th30: :: NAT_2:30
theorem Th31: :: NAT_2:31