:: SCMFSA_4 semantic presentation
theorem Th1: :: SCMFSA_4:1
theorem Th2: :: SCMFSA_4:2
:: deftheorem Def1 defines + SCMFSA_4:def 1 :
:: deftheorem Def2 defines -' SCMFSA_4:def 2 :
theorem Th3: :: SCMFSA_4:3
theorem Th4: :: SCMFSA_4:4
theorem Th5: :: SCMFSA_4:5
theorem Th6: :: SCMFSA_4:6
theorem Th7: :: SCMFSA_4:7
definition
let c
1 be
Instruction of
SCM+FSA ;
let c
2 be
Nat;
func IncAddr c
1,c
2 -> Instruction of
SCM+FSA means :
Def3:
:: SCMFSA_4:def 3
ex b
1 being
Instruction of
SCM st
( b
1 = a
1 & a
3 = IncAddr b
1,a
2 )
if InsCode a
1 in {6,7,8} otherwise a
3 = a
1;
existence
( not ( InsCode c1 in {6,7,8} & ( for b1 being Instruction of SCM+FSA
for b2 being Instruction of SCM holds
not ( b2 = c1 & b1 = IncAddr b2,c2 ) ) ) & not ( not InsCode c1 in {6,7,8} & ( for b1 being Instruction of SCM+FSA holds
not b1 = c1 ) ) )
correctness
consistency
for b1 being Instruction of SCM+FSA holds
verum;
uniqueness
for b1, b2 being Instruction of SCM+FSA holds
( ( InsCode c1 in {6,7,8} & ex b3 being Instruction of SCM st
( b3 = c1 & b1 = IncAddr b3,c2 ) & ex b3 being Instruction of SCM st
( b3 = c1 & b2 = IncAddr b3,c2 ) implies b1 = b2 ) & ( not InsCode c1 in {6,7,8} & b1 = c1 & b2 = c1 implies b1 = b2 ) );
;
end;
:: deftheorem Def3 defines IncAddr SCMFSA_4:def 3 :
theorem Th8: :: SCMFSA_4:8
theorem Th9: :: SCMFSA_4:9
theorem Th10: :: SCMFSA_4:10
theorem Th11: :: SCMFSA_4:11
theorem Th12: :: SCMFSA_4:12
theorem Th13: :: SCMFSA_4:13
theorem Th14: :: SCMFSA_4:14
theorem Th15: :: SCMFSA_4:15
theorem Th16: :: SCMFSA_4:16
theorem Th17: :: SCMFSA_4:17
theorem Th18: :: SCMFSA_4:18
theorem Th19: :: SCMFSA_4:19
theorem Th20: :: SCMFSA_4:20
theorem Th21: :: SCMFSA_4:21
theorem Th22: :: SCMFSA_4:22
:: deftheorem Def4 defines initial SCMFSA_4:def 4 :
:: deftheorem Def5 defines SCM+FSA-Stop SCMFSA_4:def 5 :
theorem Th23: :: SCMFSA_4:23
definition
let c
1 be
programmed FinPartState of
SCM+FSA ;
let c
2 be
Nat;
func IncAddr c
1,c
2 -> programmed FinPartState of
SCM+FSA means :
Def6:
:: SCMFSA_4:def 6
(
dom a
3 = dom a
1 & ( for b
1 being
Nat holds
(
insloc b
1 in dom a
1 implies a
3 . (insloc b1) = IncAddr (pi a1,(insloc b1)),a
2 ) ) );
existence
ex b1 being programmed FinPartState of SCM+FSA st
( dom b1 = dom c1 & ( for b2 being Nat holds
( insloc b2 in dom c1 implies b1 . (insloc b2) = IncAddr (pi c1,(insloc b2)),c2 ) ) )
uniqueness
for b1, b2 being programmed FinPartState of SCM+FSA holds
( dom b1 = dom c1 & ( for b3 being Nat holds
( insloc b3 in dom c1 implies b1 . (insloc b3) = IncAddr (pi c1,(insloc b3)),c2 ) ) & dom b2 = dom c1 & ( for b3 being Nat holds
( insloc b3 in dom c1 implies b2 . (insloc b3) = IncAddr (pi c1,(insloc b3)),c2 ) ) implies b1 = b2 )
end;
:: deftheorem Def6 defines IncAddr SCMFSA_4:def 6 :
theorem Th24: :: SCMFSA_4:24
theorem Th25: :: SCMFSA_4:25
theorem Th26: :: SCMFSA_4:26
theorem Th27: :: SCMFSA_4:27
theorem Th28: :: SCMFSA_4:28
theorem Th29: :: SCMFSA_4:29
:: deftheorem Def7 defines Shift SCMFSA_4:def 7 :
theorem Th30: :: SCMFSA_4:30
theorem Th31: :: SCMFSA_4:31
theorem Th32: :: SCMFSA_4:32
theorem Th33: :: SCMFSA_4:33
theorem Th34: :: SCMFSA_4:34
theorem Th35: :: SCMFSA_4:35