:: SCMPDS_9 semantic presentation
theorem Th1: :: SCMPDS_9:1
theorem Th2: :: SCMPDS_9:2
theorem Th3: :: SCMPDS_9:3
theorem Th4: :: SCMPDS_9:4
theorem Th5: :: SCMPDS_9:5
Lm1:
for f being Function
for a, b, c being set st a <> c holds
(f +* (a .--> b)) . c = f . c
by CQC_LANG:46;
Lm2:
for f being Function
for a, b, c, d being set st a <> b holds
( (f +* (a,b --> c,d)) . a = c & (f +* (a,b --> c,d)) . b = d )
by CQC_LANG:47;
Lm3:
for N being with_non-empty_elements set
for S being non empty non void IC-Ins-separated definite AMI-Struct of N
for s being State of S
for i being Instruction of S holds (Exec (s . (IC s)),s) . (IC S) = IC (Following s)
:: deftheorem Def1 defines locnum SCMPDS_9:def 1 :
theorem :: SCMPDS_9:6
canceled;
theorem :: SCMPDS_9:7
canceled;
theorem Th8: :: SCMPDS_9:8
theorem :: SCMPDS_9:9
theorem Th10: :: SCMPDS_9:10
theorem Th11: :: SCMPDS_9:11
theorem Th12: :: SCMPDS_9:12
theorem Th13: :: SCMPDS_9:13
theorem Th14: :: SCMPDS_9:14
Lm4:
for k being natural number st k > 1 holds
k - 2 is Element of NAT
theorem Th15: :: SCMPDS_9:15
theorem Th16: :: SCMPDS_9:16
theorem Th17: :: SCMPDS_9:17
theorem Th18: :: SCMPDS_9:18
theorem Th19: :: SCMPDS_9:19
theorem Th20: :: SCMPDS_9:20
theorem Th21: :: SCMPDS_9:21
theorem Th22: :: SCMPDS_9:22
theorem Th23: :: SCMPDS_9:23
theorem Th24: :: SCMPDS_9:24
theorem :: SCMPDS_9:25
theorem :: SCMPDS_9:26
theorem :: SCMPDS_9:27
Lm5:
for k being Integer holds JUMP (goto k) = {}
theorem Th28: :: SCMPDS_9:28
registration
let a,
b be
Int_position ;
let k1,
k2 be
Integer;
cluster JUMP (AddTo a,k1,b,k2) -> empty ;
coherence
JUMP (AddTo a,k1,b,k2) is empty
cluster JUMP (SubFrom a,k1,b,k2) -> empty ;
coherence
JUMP (SubFrom a,k1,b,k2) is empty
cluster JUMP (MultBy a,k1,b,k2) -> empty ;
coherence
JUMP (MultBy a,k1,b,k2) is empty
cluster JUMP (Divide a,k1,b,k2) -> empty ;
coherence
JUMP (Divide a,k1,b,k2) is empty
end;
Lm6:
not 5 / 3 is integer
Lm7:
for a being real number st a > 0 holds
- ((2 * a) + (1 + a)) < - 0
Lm8:
for d being real number holds (((2 * ((abs d) + (((- d) + (abs d)) + 4))) + 2) - 2) + (2 * d) <> - ((((2 * (((abs d) + (((- d) + (abs d)) + 4)) + (((- d) + (abs d)) + 4))) + 2) - 2) + (2 * d))
Lm9:
for b, d being real number holds (2 * b) + 2 <> (2 * b) + ((2 * (((- d) + (abs d)) + 4)) + (2 * d))
Lm10:
for c, d being real number st c > 0 holds
(2 * ((abs d) + c)) + 2 <> - (((2 * ((abs d) + c)) + (2 * c)) + (2 * d))
Lm11:
for b being real number
for d being Integer st d <> 5 holds
2 * ((b + (((- d) + (abs d)) + 4)) + 1) <> 2 * (b + d)
Lm12:
for c, d being real number st - ((2 * c) + (1 + c)) < - 0 holds
(2 * (((abs d) + c) + c)) + 2 <> - ((2 * ((abs d) + c)) + (2 * d))
Lm13:
for a being Int_position
for k1 being Integer holds JUMP (a,k1 <>0_goto 5) = {}
Lm14:
for a being Int_position
for k2, k1 being Integer st k2 <> 5 holds
JUMP (a,k1 <>0_goto k2) = {}
Lm15:
for a being Int_position
for k1 being Integer holds JUMP (a,k1 <=0_goto 5) = {}
Lm16:
for a being Int_position
for k2, k1 being Integer st k2 <> 5 holds
JUMP (a,k1 <=0_goto k2) = {}
Lm17:
for a being Int_position
for k1 being Integer holds JUMP (a,k1 >=0_goto 5) = {}
Lm18:
for a being Int_position
for k2, k1 being Integer st k2 <> 5 holds
JUMP (a,k1 >=0_goto k2) = {}
theorem Th29: :: SCMPDS_9:29
theorem Th30: :: SCMPDS_9:30