Nuprl Lemma : two-intersecting-wait-set-exists'
∀t:ℕ. ∀A:Id List.
(∃W:Id List List
((∀ws:Id List. ((ws ∈ W) ⇐⇒ (||ws|| = (t + 1) ∈ ℤ) ∧ no_repeats(Id;ws) ∧ (∀x∈ws.(x ∈ A))))
∧ (∀ws1∈W.(∀ws2∈W.∃a:Id. ((a ∈ ws1) ∧ (a ∈ ws2)))))) supposing
(no_repeats(Id;A) and
(||A|| = ((2 * t) + 1) ∈ ℤ))
Proof
Definitions occuring in Statement :
Id: Id,
l_all: (∀x∈L.P[x]),
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
length: ||as||,
list: T List,
nat: ℕ,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Lemmas :
l_member_wf,
subtype_rel_list,
list_wf,
length_wf,
no_repeats_wf,
l_all_wf2,
Id_wf,
subtype_base_sq,
list_subtype_base,
atom2_subtype_base,
select_wf,
sq_stable__le,
sq_stable__l_member,
decidable__equal_Id,
equal_wf,
int_seg_wf,
exists_wf,
iff_weakening_equal,
list-set-type2,
no_repeats-settype,
no_repeats-subtype,
nat_wf,
less_than_wf,
equal_functionality_wrt_subtype_rel2,
l_member-settype
\mforall{}t:\mBbbN{}. \mforall{}A:Id List.
(\mexists{}W:Id List List
((\mforall{}ws:Id List. ((ws \mmember{} W) \mLeftarrow{}{}\mRightarrow{} (||ws|| = (t + 1)) \mwedge{} no\_repeats(Id;ws) \mwedge{} (\mforall{}x\mmember{}ws.(x \mmember{} A))))
\mwedge{} (\mforall{}ws1\mmember{}W.(\mforall{}ws2\mmember{}W.\mexists{}a:Id. ((a \mmember{} ws1) \mwedge{} (a \mmember{} ws2)))))) supposing
(no\_repeats(Id;A) and
(||A|| = ((2 * t) + 1)))
Date html generated:
2015_07_17-AM-11_29_21
Last ObjectModification:
2015_02_04-PM-05_00_01
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