:: SCMNORM semantic presentation
registration
let
N
be
set
;
let
S
be
AMI-Struct
of
NAT
,
N
;
cluster
->
natural
Instruction-Location
of
S
;
coherence
for
b
1
being
Instruction-Location
of
S
holds
b
1
is
natural
;
end;
notation
let
N
be
set
;
let
S
be
AMI-Struct
of
NAT
,
N
;
let
l
be
Instruction-Location
of
S
;
synonym
Next
l
for
succ
N
;
end;
definition
let
N
be
set
;
let
S
be
AMI-Struct
of
NAT
,
N
;
let
l
be
Instruction-Location
of
S
;
:: original:
Next
redefine
func
Next
l
->
Instruction-Location
of
S
;
coherence
Next
is
Instruction-Location
of
S
by
AMI_1:def 4
;
end;
definition
let
N
be
set
;
let
S
be
AMI-Struct
of
NAT
,
N
;
let
l
be
Instruction-Location
of
S
;
let
k
be
Nat
;
:: original:
+
redefine
func
l
+
k
->
Instruction-Location
of
S
;
coherence
l
+
k
is
Instruction-Location
of
S
proof
end;
:: original:
-'
redefine
func
l
-'
k
->
Instruction-Location
of
S
;
coherence
l
-'
k
is
Instruction-Location
of
S
by
AMI_1:def 4
;
end;
definition
let
N
be
with_non-empty_elements
set
;
let
S
be non
empty
stored-program
definite
AMI-Struct
of
NAT
,
N
;
let
p
be
FinPartState
of
S
;
let
k
be
Element
of
NAT
;
:: original:
Shift
redefine
func
Shift
p
,
k
->
FinPartState
of
S
;
coherence
Shift
p
,
k
is
FinPartState
of
S
proof
end;
end;
registration
let
N
be
with_non-empty_elements
set
;
let
S
be non
empty
stored-program
definite
AMI-Struct
of
NAT
,
N
;
let
p
be
programmed
FinPartState
of
S
;
let
k
be
Element
of
NAT
;
cluster
Shift
p
,
k
->
programmed
FinPartState
of
S
;
coherence
Shift
p
,
k
is
programmed
FinPartState
of
S
proof
end;
end;