:: AMISTD_3 semantic presentation
theorem Th1: :: AMISTD_3:1
theorem Th2: :: AMISTD_3:2
theorem Th3: :: AMISTD_3:3
theorem Th4: :: AMISTD_3:4
theorem Th5: :: AMISTD_3:5
theorem Th6: :: AMISTD_3:6
theorem Th7: :: AMISTD_3:7
theorem Th8: :: AMISTD_3:8
theorem Th9: :: AMISTD_3:9
theorem Th10: :: AMISTD_3:10
theorem Th11: :: AMISTD_3:11
theorem Th12: :: AMISTD_3:12
Lemma54:
for O being Ordinal
for X being finite set st X c= O holds
order_type_of (RelIncl X) is finite
theorem Th13: :: AMISTD_3:13
theorem Th14: :: AMISTD_3:14
theorem Th15: :: AMISTD_3:15
theorem Th16: :: AMISTD_3:16
theorem Th17: :: AMISTD_3:17
theorem Th18: :: AMISTD_3:18
:: deftheorem Def1 defines TrivialInfiniteTree AMISTD_3:def 1 :
theorem Th19: :: AMISTD_3:19
theorem Th20: :: AMISTD_3:20
:: deftheorem Def2 defines FirstLoc AMISTD_3:def 2 :
theorem Th21: :: AMISTD_3:21
theorem Th22: :: AMISTD_3:22
theorem Th23: :: AMISTD_3:23
theorem Th24: :: AMISTD_3:24
:: deftheorem Def3 defines LocNums AMISTD_3:def 3 :
theorem Th25: :: AMISTD_3:25
theorem Th26: :: AMISTD_3:26
theorem Th27: :: AMISTD_3:27
theorem Th28: :: AMISTD_3:28
theorem Th29: :: AMISTD_3:29
theorem Th30: :: AMISTD_3:30
definition
let N be
with_non-empty_elements set ;
let S be non
empty non
void IC-Ins-separated definite standard AMI-Struct of
N;
let M be
Subset of the
Instruction-Locations of
S;
deffunc H1(
set )
-> Element of the
Instruction-Locations of
S =
il. S,
((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums M)))),(RelIncl (LocNums M))) . a1);
set Z = the
Instruction-Locations of
S;
func LocSeq c3 -> T-Sequence of the
Instruction-Locations of
a2 means :
Def4:
:: AMISTD_3:def 4
(
dom it = Card M & ( for
m being
set st
m in Card M holds
it . m = il. S,
((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums M)))),(RelIncl (LocNums M))) . m) ) );
existence
ex b1 being T-Sequence of the Instruction-Locations of S st
( dom b1 = Card M & ( for m being set st m in Card M holds
b1 . m = il. S,((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums M)))),(RelIncl (LocNums M))) . m) ) )
uniqueness
for b1, b2 being T-Sequence of the Instruction-Locations of S st dom b1 = Card M & ( for m being set st m in Card M holds
b1 . m = il. S,((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums M)))),(RelIncl (LocNums M))) . m) ) & dom b2 = Card M & ( for m being set st m in Card M holds
b2 . m = il. S,((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums M)))),(RelIncl (LocNums M))) . m) ) holds
b1 = b2
end;
:: deftheorem Def4 defines LocSeq AMISTD_3:def 4 :
theorem Th31: :: AMISTD_3:31
definition
let N be
with_non-empty_elements set ;
let S be non
empty non
void IC-Ins-separated definite standard AMI-Struct of
N;
let M be
FinPartState of
S;
func ExecTree c3 -> DecoratedTree of the
Instruction-Locations of
a2 means :
Def5:
:: AMISTD_3:def 5
(
it . {} = FirstLoc M & ( for
t being
Element of
dom it holds
(
succ t = { (t ^ <*k*>) where k is Element of NAT : k in Card (NIC (pi M,(it . t)),(it . t)) } & ( for
m being
Element of
NAT st
m in Card (NIC (pi M,(it . t)),(it . t)) holds
it . (t ^ <*m*>) = (LocSeq (NIC (pi M,(it . t)),(it . t))) . m ) ) ) );
existence
ex b1 being DecoratedTree of the Instruction-Locations of S st
( b1 . {} = FirstLoc M & ( for t being Element of dom b1 holds
( succ t = { (t ^ <*k*>) where k is Element of NAT : k in Card (NIC (pi M,(b1 . t)),(b1 . t)) } & ( for m being Element of NAT st m in Card (NIC (pi M,(b1 . t)),(b1 . t)) holds
b1 . (t ^ <*m*>) = (LocSeq (NIC (pi M,(b1 . t)),(b1 . t))) . m ) ) ) )
uniqueness
for b1, b2 being DecoratedTree of the Instruction-Locations of S st b1 . {} = FirstLoc M & ( for t being Element of dom b1 holds
( succ t = { (t ^ <*k*>) where k is Element of NAT : k in Card (NIC (pi M,(b1 . t)),(b1 . t)) } & ( for m being Element of NAT st m in Card (NIC (pi M,(b1 . t)),(b1 . t)) holds
b1 . (t ^ <*m*>) = (LocSeq (NIC (pi M,(b1 . t)),(b1 . t))) . m ) ) ) & b2 . {} = FirstLoc M & ( for t being Element of dom b2 holds
( succ t = { (t ^ <*k*>) where k is Element of NAT : k in Card (NIC (pi M,(b2 . t)),(b2 . t)) } & ( for m being Element of NAT st m in Card (NIC (pi M,(b2 . t)),(b2 . t)) holds
b2 . (t ^ <*m*>) = (LocSeq (NIC (pi M,(b2 . t)),(b2 . t))) . m ) ) ) holds
b1 = b2
end;
:: deftheorem Def5 defines ExecTree AMISTD_3:def 5 :
theorem Th32: :: AMISTD_3:32