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Theorem exists-get-def
⊦ x.exists(p) ↔ (∃ n. n < # x ∧ p(x[n]))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 19
Used lemmas:
exists-rec
,
exists-base
,
Used spec theorems:
list-del
/
get-append-grt
Used simplifier rules:
list-data
/
size-nil
nat-basic
/
less-zero
list
/
c
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04
list
/
a
nat-basic
/
succ
list
/
len-05
list-del
/
get-zero
list-data
/
l
nat-basic
/
f
list-del
/
get-succ
nat
/
lels
list-del
/
get-append-less
list
/
len-02
nat-basic
/
one-01
list-del
/
one-03
nat
/
lez
nat
/
elim-pred-c
nat
/
succ-01
nat-basic
/
oz