Nuprl Lemma : filter-interface-predecessors-lower-bound3
∀[Info:Type]
∀es:EO+(Info)
∀[T:Type]
∀X:EClass(T). ∀P:E(X) ⟶ 𝔹. ∀n:ℕ+. ∀f:ℕn ⟶ {e:E(X)| ↑P[e]} .
(∃e:{e:E(X)| ↑P[e]} . (n ≤ ||filter(λe.P[e];≤(X)(e))||)) supposing
((∀i,j:ℕn. (loc(f i) = loc(f j) ∈ Id)) and
Inj(ℕn;{e:E(X)| ↑P[e]} ;f))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
Id: Id,
length: ||as||,
filter: filter(P;l),
inject: Inj(A;B;f),
int_seg: {i..j-},
nat_plus: ℕ+,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
inject: Inj(A;B;f),
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
so_apply: x[s],
prop: ℙ,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
es-E-interface: E(X),
exists: ∃x:A. B[x]
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}P:E(X) {}\mrightarrow{} \mBbbB{}. \mforall{}n:\mBbbN{}\msupplus{}. \mforall{}f:\mBbbN{}n {}\mrightarrow{} \{e:E(X)| \muparrow{}P[e]\} .
(\mexists{}e:\{e:E(X)| \muparrow{}P[e]\} . (n \mleq{} ||filter(\mlambda{}e.P[e];\mleq{}(X)(e))||)) supposing
((\mforall{}i,j:\mBbbN{}n. (loc(f i) = loc(f j))) and
Inj(\mBbbN{}n;\{e:E(X)| \muparrow{}P[e]\} ;f))
Date html generated:
2016_05_17-AM-07_06_15
Last ObjectModification:
2015_12_29-AM-00_14_10
Theory : event-ordering
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