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Theorem diffone-nodupsget
⊦ n + 1 < # x ∧ ¬ dups(x) ∧ a ∈ x → (x \ a ')[n] = (n < pos(a, x) ⊃ x[n];x[n + 1])
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 18
Used lemmas:
diff-n
,
diff-y
,
diff-onenonmember
,
diff-firstofapp
,
Used spec theorems:
list-del
/
get-append-grt
Used simplifier rules:
list-del
/
pos-n
list-del
/
get-nodups
nat-basic1
/
zero-01
list-del
/
pos-y
list-data
/
l
list-dup
/
rec
nat-basic2
/
l
list
/
len-05
list
/
in-rec
list
/
e-01
list-del
/
get-succ
list
/
in-17
list
/
c
list-del
/
inl
nat-basic2
/
succ
nat-basic1
/
trans-1
nat-basic1
/
lf
nat
/
elim-pred-c
nat-basic2
/
s
nat
/
le-ls-simp
nat
/
lels
list-del
/
get-append-less
nat-basic1
/
one-01
list
/
a
list-del
/
get-append-grt
list
/
len-02
nat-basic1
/
f
nat
/
succ-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
oz