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Theorem to-to-leq
¬ # σ < ⌜n⌝ ⊦ m ≤ n → σ to n to m = σ to m
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
to-to-eq
,
to-to-ls
,
toinf-to-leq
,
Used by units in proved state:
mon-lim-filter-count
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 19
Used lemmas:
to-to-leq-inf
,
to-inf
,
length-to
,
append-to-le
,
to-unwind-end-fin
,
to-zero-l
,
size-fin
,
to-fin
,
Used spec theorems:
list-del
/
get-append-grt
Used simplifier rules:
nat
/
let
nat-inf
/
less-fin
stream-basic
/
inj-02
nat
/
lez-01
nat
/
lez
list-data
/
l
nat-basic2
/
succ
nat
/
succ-01
nat
/
lep-02
nat-basic2
/
oz
nat
/
fle
nat-basic1
/
lf-01
nat-basic1
/
f
nat
/
eqle-one
nat
/
les
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
s
list
/
len-02
list
/
len
list-del
/
get-butlast
nat
/
lels
list-del
/
one-03
nat
/
zero
list
/
a
list
/
app-03
nat
/
lels-01
nat-basic1
/
ref-1
nat
/
ler
nat
/
fle-01
nat-basic1
/
ls-02
nat
/
lels-03