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Theorem stutf-maxinf-is-fin
⊦ stutf(nσ) → (max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m) = ∞ ↔ # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m) ∨ (∀ n. ⌜n⌝ < # nσ → nσ[n] < m))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
inv-get-inverse-last
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 17
Proof steps: 36
Used lemmas:
stutf-monle
,
monle-leq
,
stutf-alltaken
,
maxinf-inf
,
Used spec theorems:
nat-inf-basic
/
notinf-fin
Used simplifier rules:
nat
/
lels
nat
/
lels-02
nat
/
fle-01
nat-basic1
/
lf-02
nat
/
lels-03
nat-inf
/
less-inf2
nat
/
ls-le-simp
nat-basic1
/
lf
nat-basic1
/
trans-1
nat-basic1
/
ls-02
nat-inf
/
lsle-trans
nat-inf
/
less-fin
nat
/
le-ls-simp
nat-basic1
/
ref-1
nat-basic2
/
s
nat-basic2
/
succ
nat-basic1
/
f
nat
/
fle
nat-basic2
/
l-02
nat-basic2
/
a
nat-basic2
/
c