:: 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
Lemma9:
for b1 being Ordinal
for b2 being finite set holds
( b2 c= b1 implies order_type_of (RelIncl b2) 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 c
1 be
with_non-empty_elements set ;
let c
2 be non
empty non
void IC-Ins-separated definite standard AMI-Struct of c
1;
let c
3 be
Subset of the
Instruction-Locations of c
2;
deffunc H
1(
set )
-> Element of the
Instruction-Locations of c
2 =
il. c
2,
((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums c3)))),(RelIncl (LocNums c3))) . a1);
set c
4 = the
Instruction-Locations of c
2;
func LocSeq c
3 -> T-Sequence of the
Instruction-Locations of a
2 means :
Def4:
:: AMISTD_3:def 4
(
dom a
4 = Card a
3 & ( for b
1 being
set holds
( b
1 in Card a
3 implies a
4 . b
1 = il. a
2,
((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums a3)))),(RelIncl (LocNums a3))) . b1) ) ) );
existence
ex b1 being T-Sequence of the Instruction-Locations of c2 st
( dom b1 = Card c3 & ( for b2 being set holds
( b2 in Card c3 implies b1 . b2 = il. c2,((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums c3)))),(RelIncl (LocNums c3))) . b2) ) ) )
uniqueness
for b1, b2 being T-Sequence of the Instruction-Locations of c2 holds
( dom b1 = Card c3 & ( for b3 being set holds
( b3 in Card c3 implies b1 . b3 = il. c2,((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums c3)))),(RelIncl (LocNums c3))) . b3) ) ) & dom b2 = Card c3 & ( for b3 being set holds
( b3 in Card c3 implies b2 . b3 = il. c2,((canonical_isomorphism_of (RelIncl (order_type_of (RelIncl (LocNums c3)))),(RelIncl (LocNums c3))) . b3) ) ) implies b1 = b2 )
end;
:: deftheorem Def4 defines LocSeq AMISTD_3:def 4 :
theorem Th31: :: AMISTD_3:31
definition
let c
1 be
with_non-empty_elements set ;
let c
2 be non
empty non
void IC-Ins-separated definite standard AMI-Struct of c
1;
let c
3 be
FinPartState of c
2;
func ExecTree c
3 -> DecoratedTree of the
Instruction-Locations of a
2 means :
Def5:
:: AMISTD_3:def 5
( a
4 . {} = FirstLoc a
3 & ( for b
1 being
Element of
dom a
4 holds
(
succ b
1 = { (b1 ^ <*b2*>) where B is Nat : b2 in Card (NIC (pi a3,(a4 . b1)),(a4 . b1)) } & ( for b
2 being
Nat holds
( b
2 in Card (NIC (pi a3,(a4 . b1)),(a4 . b1)) implies a
4 . (b1 ^ <*b2*>) = (LocSeq (NIC (pi a3,(a4 . b1)),(a4 . b1))) . b
2 ) ) ) ) );
existence
ex b1 being DecoratedTree of the Instruction-Locations of c2 st
( b1 . {} = FirstLoc c3 & ( for b2 being Element of dom b1 holds
( succ b2 = { (b2 ^ <*b3*>) where B is Nat : b3 in Card (NIC (pi c3,(b1 . b2)),(b1 . b2)) } & ( for b3 being Nat holds
( b3 in Card (NIC (pi c3,(b1 . b2)),(b1 . b2)) implies b1 . (b2 ^ <*b3*>) = (LocSeq (NIC (pi c3,(b1 . b2)),(b1 . b2))) . b3 ) ) ) ) )
uniqueness
for b1, b2 being DecoratedTree of the Instruction-Locations of c2 holds
( b1 . {} = FirstLoc c3 & ( for b3 being Element of dom b1 holds
( succ b3 = { (b3 ^ <*b4*>) where B is Nat : b4 in Card (NIC (pi c3,(b1 . b3)),(b1 . b3)) } & ( for b4 being Nat holds
( b4 in Card (NIC (pi c3,(b1 . b3)),(b1 . b3)) implies b1 . (b3 ^ <*b4*>) = (LocSeq (NIC (pi c3,(b1 . b3)),(b1 . b3))) . b4 ) ) ) ) & b2 . {} = FirstLoc c3 & ( for b3 being Element of dom b2 holds
( succ b3 = { (b3 ^ <*b4*>) where B is Nat : b4 in Card (NIC (pi c3,(b2 . b3)),(b2 . b3)) } & ( for b4 being Nat holds
( b4 in Card (NIC (pi c3,(b2 . b3)),(b2 . b3)) implies b2 . (b3 ^ <*b4*>) = (LocSeq (NIC (pi c3,(b2 . b3)),(b2 . b3))) . b4 ) ) ) ) implies b1 = b2 )
end;
:: deftheorem Def5 defines ExecTree AMISTD_3:def 5 :
theorem Th32: :: AMISTD_3:32