begin
definition
let R be ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ;
func SCM R -> ( (
strict ) (
strict )
AMI-Struct over 2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) )
means
( the
carrier of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( ( ) ( )
set )
= SCM-Memory : ( ( ) ( non
empty )
set ) & the
ZeroF of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of the
carrier of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
= NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) & the
InstructionsF of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set )
= SCM-Instr R : ( ( ) ( )
set ) : ( ( non
empty ) ( non
empty )
set ) & the
Object-Kind of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( ( ) ( )
set )
-defined 2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-valued Function-like quasi_total )
Element of
K27(
K28( the
carrier of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ,2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
= SCM-OK : ( (
Function-like quasi_total ) (
Relation-like SCM-Memory : ( ( ) ( non
empty )
set )
-defined 2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-valued Function-like quasi_total )
Element of
K27(
K28(
SCM-Memory : ( ( ) ( non
empty )
set ) ,2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) & the
ValuesF of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( (
Relation-like 2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-defined Function-like V35(2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) ) ) (
Relation-like 2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-defined Function-like V35(2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) ) )
set )
= SCM-VAL R : ( ( ) ( )
set ) : ( (
Relation-like 2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-defined Function-like V35(2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) ) ) (
Relation-like 2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-defined Function-like V35(2 : ( ( ) (
V6()
V7()
V8()
V12() non
empty V62()
V164() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) ) )
set ) & the
Execution of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( (
Function-like quasi_total ) (
Relation-like the
InstructionsF of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set )
-defined Funcs (
(product ( the Object-Kind of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( Function-like quasi_total ) ( Relation-like the carrier of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) -defined 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -valued Function-like quasi_total ) Element of K27(K28( the carrier of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ,2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) * the ValuesF of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) set ) ) : ( ( Relation-like ) ( Relation-like Function-like ) set ) ) : ( ( ) (
functional with_common_domain product-like )
set ) ,
(product ( the Object-Kind of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( Function-like quasi_total ) ( Relation-like the carrier of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) -defined 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -valued Function-like quasi_total ) Element of K27(K28( the carrier of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ,2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) * the ValuesF of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) set ) ) : ( ( Relation-like ) ( Relation-like Function-like ) set ) ) : ( ( ) (
functional with_common_domain product-like )
set ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Element of
K27(
K28( the
InstructionsF of
it : ( ( ) ( )
AMI-Struct over
R : ( ( ) ( )
set ) ) : ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ,
(Funcs ((product ( the Object-Kind of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( Function-like quasi_total ) ( Relation-like the carrier of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) -defined 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -valued Function-like quasi_total ) Element of K27(K28( the carrier of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ,2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) * the ValuesF of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) set ) ) : ( ( Relation-like ) ( Relation-like Function-like ) set ) ) : ( ( ) ( functional with_common_domain product-like ) set ) ,(product ( the Object-Kind of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( Function-like quasi_total ) ( Relation-like the carrier of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) -defined 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -valued Function-like quasi_total ) Element of K27(K28( the carrier of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ,2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) * the ValuesF of it : ( ( ) ( ) AMI-Struct over R : ( ( ) ( ) set ) ) : ( ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) set ) ) : ( ( Relation-like ) ( Relation-like Function-like ) set ) ) : ( ( ) ( functional with_common_domain product-like ) set ) )) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
= SCM-Exec R : ( ( ) ( )
set ) : ( (
Function-like quasi_total ) (
Relation-like SCM-Instr R : ( ( ) ( )
set ) : ( ( non
empty ) ( non
empty )
set )
-defined Funcs (
(product (SCM-OK : ( ( Function-like quasi_total ) ( Relation-like SCM-Memory : ( ( ) ( non empty ) set ) -defined 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -valued Function-like quasi_total ) Element of K27(K28(SCM-Memory : ( ( ) ( non empty ) set ) ,2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) * (SCM-VAL R : ( ( ) ( ) set ) ) : ( ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) set ) ) : ( ( Relation-like ) ( Relation-like Function-like ) set ) ) : ( ( ) (
functional with_common_domain product-like )
set ) ,
(product (SCM-OK : ( ( Function-like quasi_total ) ( Relation-like SCM-Memory : ( ( ) ( non empty ) set ) -defined 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -valued Function-like quasi_total ) Element of K27(K28(SCM-Memory : ( ( ) ( non empty ) set ) ,2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) * (SCM-VAL R : ( ( ) ( ) set ) ) : ( ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) set ) ) : ( ( Relation-like ) ( Relation-like Function-like ) set ) ) : ( ( ) (
functional with_common_domain product-like )
set ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Element of
K27(
K28(
(SCM-Instr R : ( ( ) ( ) set ) ) : ( ( non
empty ) ( non
empty )
set ) ,
(Funcs ((product (SCM-OK : ( ( Function-like quasi_total ) ( Relation-like SCM-Memory : ( ( ) ( non empty ) set ) -defined 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -valued Function-like quasi_total ) Element of K27(K28(SCM-Memory : ( ( ) ( non empty ) set ) ,2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) * (SCM-VAL R : ( ( ) ( ) set ) ) : ( ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) set ) ) : ( ( Relation-like ) ( Relation-like Function-like ) set ) ) : ( ( ) ( functional with_common_domain product-like ) set ) ,(product (SCM-OK : ( ( Function-like quasi_total ) ( Relation-like SCM-Memory : ( ( ) ( non empty ) set ) -defined 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -valued Function-like quasi_total ) Element of K27(K28(SCM-Memory : ( ( ) ( non empty ) set ) ,2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) * (SCM-VAL R : ( ( ) ( ) set ) ) : ( ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) ( Relation-like 2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -defined Function-like V35(2 : ( ( ) ( V6() V7() V8() V12() non empty V62() V164() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ) set ) ) : ( ( Relation-like ) ( Relation-like Function-like ) set ) ) : ( ( ) ( functional with_common_domain product-like ) set ) )) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) );
end;
theorem
for
R being ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring)
for
I being ( ( ) ( )
set ) holds
(
I : ( ( ) ( )
set ) is ( ( ) ( )
Instruction of ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ) iff (
I : ( ( ) ( )
set )
= [0 : ( ( ) ( V6() V7() V8() V12() ) Element of NAT : ( ( ) ( V6() V7() V8() non empty V24() countable denumerable ) Element of K27(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,{} : ( ( ) ( ) set ) ,{} : ( ( ) ( ) set ) ] : ( ( ) (
V21()
V22() )
set ) or ex
a,
b being ( (
Int-like ) (
Int-like )
Data-Location of
R : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) st
I : ( ( ) ( )
set )
= a : ( (
Int-like ) (
Int-like )
Data-Location of
b1 : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) )
:= b : ( ( ) ( )
Element of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Instruction of ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ) or ex
a,
b being ( (
Int-like ) (
Int-like )
Data-Location of
R : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) st
I : ( ( ) ( )
set )
= AddTo (
a : ( (
Int-like ) (
Int-like )
Data-Location of
b1 : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) ,
b : ( ( ) ( )
Element of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Instruction of ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ) or ex
a,
b being ( (
Int-like ) (
Int-like )
Data-Location of
R : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) st
I : ( ( ) ( )
set )
= SubFrom (
a : ( (
Int-like ) (
Int-like )
Data-Location of
b1 : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) ,
b : ( ( ) ( )
Element of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Instruction of ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ) or ex
a,
b being ( (
Int-like ) (
Int-like )
Data-Location of
R : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) st
I : ( ( ) ( )
set )
= MultBy (
a : ( (
Int-like ) (
Int-like )
Data-Location of
b1 : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) ,
b : ( ( ) ( )
Element of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Instruction of ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ) or ex
i1 being ( ( ) (
V6()
V7()
V8()
V12() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) st
I : ( ( ) ( )
set )
= goto (
i1 : ( (
Int-like ) (
Int-like )
Data-Location of
b1 : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) ,
R : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) : ( ( ) ( )
Instruction of ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ) or ex
a being ( (
Int-like ) (
Int-like )
Data-Location of
R : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) ex
i1 being ( ( ) (
V6()
V7()
V8()
V12() )
Element of
NAT : ( ( ) (
V6()
V7()
V8() non
empty V24()
countable denumerable )
Element of
K27(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) st
I : ( ( ) ( )
set )
= a : ( (
Int-like ) (
Int-like )
Data-Location of
b1 : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) )
=0_goto i1 : ( ( ) ( )
Element of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Instruction of ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ) or ex
a being ( (
Int-like ) (
Int-like )
Data-Location of
R : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) ) ex
r being ( ( ) ( )
Element of ( ( ) ( non
empty )
set ) ) st
I : ( ( ) ( )
set )
= a : ( (
Int-like ) (
Int-like )
Data-Location of
b1 : ( ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() ) ( non
empty V106()
V131()
V132()
V133()
V141()
V148()
V149() )
Ring) )
:= r : ( ( ) ( )
Element of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Instruction of ( (
standard-ins V71()
V72()
V74() ) (
standard-ins V71()
V72()
V74() )
set ) ) ) ) ;
begin
begin