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Theorem in-prefixn-pos-smaller
⊦ a ∈ prefixn(n, x) → pos(a, x) < n
Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
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: 7
Used lemmas:
prefixn
,
Used spec theorems:
Used simplifier rules:
list-del
/
len-01
nat
/
fle
nat
/
le-def
list-del
/
pos-e
nat
/
lez-01
nat
/
lez
list-del
/
firstN-zero
list
/
in-empty
nat
/
lels
nat-basic
/
s-04
list-del
/
pos-n
nat-basic
/
zero-01
list-del
/
pos-y
nat-basic
/
f
list
/
in-rec
list
/
a
list
/
c
list-del
/
weak-firstN-rec
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
nat-basic
/
succ