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Theorem add-lastrec
⊦ vals ≠ [] → addarray(r, ty, vals, st) = (addarray(r, ty, vals .butlast, st)[r -- n→i((# vals) -1) ', vals .last][r -- _length, intval(n→i(# vals))])
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
add-at-gr
,
add-at-neg
,
add-in-fskey
,
add-isobj
,
add-refs
,
addarray-both-subset
,
addarray-mklist-05
,
addarray-mode
,
addbar-refval-01
,
in-add
,
move-initvals
,
putarray-add-butlast
,
switch-array
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 20
Used lemmas:
init-last
,
init-switch
,
addarrayinit-def
,
Used spec theorems:
store
/javastore/
rew
Used simplifier rules:
int-basic2
/
add-c
int-basic2
/
ax-04
int-basic2
/
add-a
refkey
/
inj-01
refkey
/
inj
specialkeys
/
type-03
store
/javastore/
ins3
specialkeys
/
type-06
specialkeys
/
length-04
list
/javavalues/
e-02
nat-basic2
/
eq-01
list
/javavalues/
a
list
/javavalues/
len-02
list
/javavalues/
len
list-last
/javavalues/
last-elim
nat-basic2
/
z
nat
/
add-01
list-last
/javavalues/
lb
nat-basic2
/
c
nat-basic2
/
a
intnat
/
n2i-add
nat
/
pred-03
list-data
/javavalues/
l
nat
/
elim-pred-c