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Theorem leninv-inf
⊦ stutf(nσ) → (leninv(nσ) = ∞ ↔ # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
inv-get-inverse
,
inv-get-inverse-between
,
inv-get-inverse-succ
,
inv-inverts-leq
,
inv-ls-succ
,
leninv-inf-strong
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 28
Proof steps: 59
Used lemmas:
stutf-nonempty
,
stutf-alltaken
,
stutf-zero
,
stutf-monle
,
monle-leq
,
maxinf-inf
,
leninv-def
,
Used spec theorems:
nat-inf-basic
/
notinf-fin
Used simplifier rules:
nat
/
l-num-06
nat
/
elim-pred-c
nat-basic2
/
l
nat
/
eq
nat
/
lels-01
nat-basic2
/
eq
nat
/
eqle-one
nat-inf
/
less-inf2
nat
/
succ-01
stream
/natstream/
size-empty-equiv
nat-inf
/
add-fin
nat-basic2
/
succ
nat-basic1
/
f
nat
/
lels
nat-inf
/
add-assoc
nat-inf
/
add-comm
nat-inf
/
inf-inseq-reduce
nat-basic2
/
s
nat
/
ls-le-simp
nat-basic2
/
add-base
nat
/
add-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
oz
nat-basic1
/
ref-1