:: SCM_1 semantic presentation
theorem :: SCM_1:1
canceled;
theorem :: SCM_1:2
theorem Th3: :: SCM_1:3
theorem Th4: :: SCM_1:4
theorem :: SCM_1:5
canceled;
theorem :: SCM_1:6
canceled;
theorem Th7: :: SCM_1:7
:: deftheorem Def1 defines State-consisting SCM_1:def 1 :
theorem :: SCM_1:8
canceled;
theorem :: SCM_1:9
canceled;
theorem :: SCM_1:10
canceled;
theorem :: SCM_1:11
canceled;
theorem :: SCM_1:12
canceled;
theorem :: SCM_1:13
canceled;
theorem :: SCM_1:14
for
I1,
I2,
I3,
I4,
I5,
I6,
I7,
I8,
I9 being
Instruction of
SCM for
i1,
i2,
i3,
i4 being
Integer for
il being
Element of
NAT for
s being
State-consisting of
il,0,0,
(((((((<*I1*> ^ <*I2*>) ^ <*I3*>) ^ <*I4*>) ^ <*I5*>) ^ <*I6*>) ^ <*I7*>) ^ <*I8*>) ^ <*I9*>,
((<*i1*> ^ <*i2*>) ^ <*i3*>) ^ <*i4*> holds
(
IC s = il. il &
s . (il. 0) = I1 &
s . (il. 1) = I2 &
s . (il. 2) = I3 &
s . (il. 3) = I4 &
s . (il. 4) = I5 &
s . (il. 5) = I6 &
s . (il. 6) = I7 &
s . (il. 7) = I8 &
s . (il. 8) = I9 &
s . (dl. 0) = i1 &
s . (dl. 1) = i2 &
s . (dl. 2) = i3 &
s . (dl. 3) = i4 )
theorem Th15: :: SCM_1:15
theorem Th16: :: SCM_1:16
theorem Th17: :: SCM_1:17
Lm3:
for n being Element of NAT holds Next (il. n) = il. (n + 1)
Lm4:
for k being Element of NAT
for s being State of SCM holds (Computation s) . (k + 1) = Exec (CurInstr ((Computation s) . k)),((Computation s) . k)
Lm5:
now
let k,
n be
Element of
NAT ;
let s be
State of
SCM ;
let a,
b be
Data-Location ;
assume A1:
IC ((Computation s) . k) = il. n
;
set csk =
(Computation s) . k;
set csk1 =
(Computation s) . (k + 1);
assume A2:
(
s . (il. n) = a := b or
s . (il. n) = AddTo a,
b or
s . (il. n) = SubFrom a,
b or
s . (il. n) = MultBy a,
b or (
a <> b &
s . (il. n) = Divide a,
b ) )
;
thus (Computation s) . (k + 1) =
Exec (CurInstr ((Computation s) . k)),
((Computation s) . k)
by Lm4
.=
Exec (s . (il. n)),
((Computation s) . k)
by A1, AMI_1:54
;
hence IC ((Computation s) . (k + 1)) =
Next (IC ((Computation s) . k))
by A2, AMI_3:8, AMI_3:9, AMI_3:10, AMI_3:11, AMI_3:12
.=
il. (n + 1)
by A1, Lm3
;
end;
theorem Th18: :: SCM_1:18
theorem Th19: :: SCM_1:19
theorem Th20: :: SCM_1:20
theorem Th21: :: SCM_1:21
theorem Th22: :: SCM_1:22
theorem Th23: :: SCM_1:23
theorem Th24: :: SCM_1:24
theorem Th25: :: SCM_1:25
theorem Th26: :: SCM_1:26
theorem :: SCM_1:27
canceled;
theorem :: SCM_1:28
theorem :: SCM_1:29
theorem :: SCM_1:30
for
I1,
I2,
I3,
I4,
I5,
I6,
I7,
I8,
I9 being
Instruction of
SCM for
i1,
i2,
i3,
i4 being
Integer for
il being
Element of
NAT for
s being
State of
SCM st
IC s = il. il &
s . (il. 0) = I1 &
s . (il. 1) = I2 &
s . (il. 2) = I3 &
s . (il. 3) = I4 &
s . (il. 4) = I5 &
s . (il. 5) = I6 &
s . (il. 6) = I7 &
s . (il. 7) = I8 &
s . (il. 8) = I9 &
s . (dl. 0) = i1 &
s . (dl. 1) = i2 &
s . (dl. 2) = i3 &
s . (dl. 3) = i4 holds
s is
State-consisting of
il,0,0,
(((((((<*I1*> ^ <*I2*>) ^ <*I3*>) ^ <*I4*>) ^ <*I5*>) ^ <*I6*>) ^ <*I7*>) ^ <*I8*>) ^ <*I9*>,
((<*i1*> ^ <*i2*>) ^ <*i3*>) ^ <*i4*>
theorem :: SCM_1:31
theorem :: SCM_1:32
theorem :: SCM_1:33
theorem :: SCM_1:34
theorem :: SCM_1:35
theorem :: SCM_1:36
theorem :: SCM_1:37
theorem :: SCM_1:38
theorem :: SCM_1:39