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Theorem inv-get-inverse-between
⊦ stutf(nσ) ∧ ⌜n⌝ + ⌜1⌝ < leninv(nσ) ∧ inv(nσ)[n] + m + 1 < inv(nσ)[n + 1] → nσ[inv(nσ)[n] + m + 1] = n + 1
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: 78
Proof steps: 166
Used lemmas:
stutf-nonempty
,
stutf-def
,
leninv-succ
,
stutf-alltaken
,
stutf-zero
,
maxinf-fin
,
stutf-monle
,
monle-leq
,
maxinf-inf
,
leninv-inf
,
leninv-inf-strong
,
inv-def
,
Used spec theorems:
Used simplifier rules:
stream
/natstream/
to-inf
stream
/natstream/
sel-inf
nat-inf-basic
/
elim
nat-basic1
/
trans-1
nat
/
ls-03
nat-basic1
/
one-01
nat
/
pred-03
nat
/
ler
nat-basic2
/
l-02
stream
/natstream/
sel-fin
nat-inf
/
leq-notgradd
stream
/natstream/
get-infto
nat-basic2
/
l
nat-basic2
/
eqs
nat
/
eq
nat
/
lels-01
nat-inf
/
less-inf2
nat-inf
/
addeqinf-cancel
nat-inf
/
inf-less
nat-inf-basic
/
disj
stream
/natstream/
size-empty-equiv
nat
/
elim-pred-c
nat-basic1
/
lf-02
nat
/
lels-03
nat
/
eqle-one
nat
/
anti
nat
/
fle
nat-basic2
/
nls-fst
nat-inf
/
inf-inseq-reduce
nat
/
succ-01
nat-basic2
/
eq
nat-basic2
/
oz
nat-inf
/
num-add
nat
/
lep-02
nat-inf
/
add-ls-cancel-num-04
nat-inf
/
add-all-zero
nat-inf
/
ls-natinf-to-nat-2-1
nat
/
lels
nat
/
le-ls-simp
nat-basic1
/
lf-01
nat
/
let
nat
/
fle-01
nat-basic2
/
succ-03
nat-inf
/
less-succ-leq
nat
/
les
nat-basic2
/
succ
nat-basic1
/
lf
nat-basic1
/
f
nat
/
lels-02
nat-basic1
/
ref-1
nat-basic2
/
s
nat-basic1
/
ls-02
nat-basic2
/
neq-01
nat
/
lep
nat-basic2
/
a
nat-basic2
/
c
nat-inf
/
add-fin
nat-inf
/
add-assoc
nat-inf
/
add-comm
nat-inf
/
eqls-succ
nat-inf
/
less-fin
nat
/
ls-le-simp