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Theorem rmpos-in
⊦ ¬ dups(x) ∧ n < # x → (a ∈ x -1l n ↔ a ≠ x[n] ∧ a ∈ x)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
nodups-rmposnodups
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 36
Used lemmas:
get-in
,
delpos-rec
,
delpos-base
,
get-zero-01
,
get-append-grt
,
one-03
,
delnr-one
,
Used spec theorems:
Used simplifier rules:
nat
/
lels
list-dup
/
rec
nat-basic2
/
s
list
/
len-05
list
/
e-01
list
/
app
list
/
in-empty
list-data
/
size-01
nat
/
lez-01
list-dup
/
e-01
nat-basic1
/
zero-01
nat
/
lez
list
/
len-02
nat-basic1
/
one-01
list
/
in-rec
list
/
in-01
nat-basic2
/
succ
list-data
/
l
nat-basic1
/
f
nat-basic2
/
oz
nat-basic2
/
a
nat-basic2
/
c
nat
/
succ-01
list
/
c
list
/
a
list
/
in-06
nat
/
elim-pred-c