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Theorem maxinf-skolemf
⊦ ∃ n∞. (n∞ = ∞ ⊃ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n));(∃ n. np(n∞.n)) ∧ (∀ m. np(m) → ¬ n∞ < ⌜m⌝ ))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: justifies definition of max∞
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 13
Proof steps: 31
Used lemmas:
Used spec theorems:
Used simplifier rules:
nat-inf
/
less-fin
nat-inf-basic
/
sel
nat-inf-basic
/
disj
nat
/
elim-sub
nat
/
lep
nat
/
lez
nat
/
ls-01
nat
/
leprf
nat
/
lels-01
nat
/
le-one
nat-basic1
/
f
nat-basic1
/
lf
nat-basic1
/
lf-01
nat-basic1
/
trans-1
nat-basic1
/
lf-02
nat
/
fle
nat
/
ler
nat
/
le-add
nat
/
ls-le-simp
nat
/
ls-02
nat
/
eq
nat-basic2
/
z-01
nat
/
elim-pred-c
nat
/
succ-01
nat-basic2
/
oz
nat
/
eqle-one
nat
/
lels
nat
/
les
nat-basic2
/
a
nat-basic2
/
c