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Theorem in-prefixn-pos-smaller0
⊦ a ∈ prefixn(n, x) ∧ m ≤ pos(a, x) → m ≤ n
Type: A user defined theorem
Validity: The proof is valid.
Features: forward,
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-basic
/
trans
nat-basic
/
lf
nat
/
le-def
list-del
/
pos-e
list-del
/
firstN-zero
list
/
in-empty
nat-basic
/
l
list-del
/
pos-n
nat-basic
/
f
nat
/
lez-01
list-del
/
pos-y
nat
/
fle
list
/
in-rec
nat-basic
/
c
nat-basic
/
a
list
/
a
list
/
c
list-del
/
weak-firstN-rec
nat-basic
/
succ
nat
/
ler