Nuprl Lemma : three-intersecting-wait-set-exists
∀t:ℕ. ∀A:Id List.
(∃W:{a:Id| (a ∈ A)} List List
((∀ws:{a:Id| (a ∈ A)} List. ((ws ∈ W) ⇐⇒ (||ws|| = ((2 * t) + 1) ∈ ℤ) ∧ no_repeats({a:Id| (a ∈ A)} ;ws)))
∧ three-intersection(A;W))) supposing
(no_repeats(Id;A) and
(||A|| = ((3 * t) + 1) ∈ ℤ))
Proof
Definitions occuring in Statement :
three-intersection: three-intersection(A;W),
Id: Id,
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,
set: {x:A| B[x]} ,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Lemmas :
no_repeats_witness,
Id_wf,
combinations-list,
all_wf,
list_wf,
iff_wf,
l_member_wf,
length_wf,
no_repeats_wf,
three-intersection_wf,
equal_wf,
nat_wf,
int_seg_wf,
decidable__equal_Id,
length_wf_nat,
equipollent_functionality_wrt_equipollent,
equipollent-length,
equipollent_weakening_ext-eq,
ext-eq_weakening,
equipollent-nsub,
three-intersecting-wait-set
\mforall{}t:\mBbbN{}. \mforall{}A:Id List.
(\mexists{}W:\{a:Id| (a \mmember{} A)\} List List
((\mforall{}ws:\{a:Id| (a \mmember{} A)\} List. ((ws \mmember{} W) \mLeftarrow{}{}\mRightarrow{} (||ws|| = ((2 * t) + 1)) \mwedge{} no\_repeats(\{a:Id| (a \mmember{} A)\}\000C ;ws)))
\mwedge{} three-intersection(A;W))) supposing
(no\_repeats(Id;A) and
(||A|| = ((3 * t) + 1)))
Date html generated:
2015_07_17-AM-11_29_11
Last ObjectModification:
2015_01_28-AM-01_34_33
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