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Theorem finfrag-pis-init
⊦ frag*(IOAut(Π(lstart, rstart), Π(lstep, rstep, lren, rren, lext, rext), Π(lext, rext, lren, rren)))(psl, pal) → πrs(lstep, rstep, lren, rren, psl, pal) ≠ [] ∧ πrs(lstep, rstep, lren, rren, psl, pal).head = psl.head._2
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
finfrag-init
,
finfrag-pis-nonempty
,
proj-exec-fin
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 30
Used lemmas:
projstate-rec-addboth
,
projstate-rec-addR
,
projstate-rec-skipL
,
projstate-base
,
Used spec theorems:
IOtrace
/
frag
IOtrace
/
frag-rec
product
/
lrstep-def
Used simplifier rules:
stream
/
empty
IOtrace
/
not-frag-empty
list
/
a
list
/
c-08
list
/
c
stream
/
append-finfin
list
/
app
nat-basic
/
less-zero
nat-inf
/
less-fin
stream
/
size-empty
nat-inf
/
add-comm
nat-inf
/
add-assoc
list-data
/
l
nat-inf
/
inj-rqui
nat-inf
/
add-cancel-num-01
nat-basic
/
c
nat-basic
/
a
nat-inf
/
num-add
stream
/
append-assoc
stream
/
size-fin
list
/
len-02
stream
/
size-append
list
/
e
list
/
first
list-data
/
elim-add
list
/
in-14
stream
/
hd-fin-lem
list
/
in-rec
list
/
app-02
IOtrace
/
fragfin-size-02