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Theorem min-skolemf
⊦ mon<(nσ) → (∃ m0. (nσ = [] ⊃ m0 = 0 ;(# nσ ≠ ∞ ∧ nσ[(# nσ).n - 1] < n ⊃ m0 = (# nσ).n;⌜m0⌝ < # nσ ∧ n ≤ nσ[m0] ∧ (∀ m. ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → m0 ≤ m)) ))
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: 16
Proof steps: 37
Used lemmas:
monls-def
,
Used spec theorems:
Used simplifier rules:
nat-basic1
/
zero-01
stream
/natstream/
zero-len
nat
/
lez
nat-basic2
/
succ
nat
/
lels-02
nat-basic1
/
ls-02
nat
/
lels-01
nat
/
ls-le-simp
nat
/
succ-01
nat-inf
/
add-fin
nat
/
le-ls-simp
nat
/
lels
nat
/
lels-03
nat
/
anti
nat
/
ler
nat-basic1
/
f
nat-inf
/
sum-notinf
nat-basic2
/
s
nat-inf
/
inf-inseq-reduce
nat-inf
/
ls-notlssucc
nat-inf-basic
/
disj
nat-inf
/
prime-add-fin
nat-inf-basic
/
sel
nat-inf
/
add-assoc
nat-inf
/
add-comm
nat
/
add-01
nat-basic2
/
add-base
nat-basic2
/
a
nat-basic2
/
c
nat-basic1
/
ref-1