Nuprl Lemma : filter-interface-predecessors-lower-bound-implies
∀[Info:Type]
∀es:EO+(Info)
∀[T:Type]
∀X:EClass(T). ∀P:E(X) ⟶ 𝔹. ∀n:ℕ. ∀e:E.
∃f:ℕn ⟶ {e':E(X)| (↑P[e']) ∧ e' ≤loc e } . ∀i,j:ℕn. (f i <loc f j) supposing i < j
supposing n ≤ ||filter(λe.P[e];≤(X)(e))||
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-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
length: ||as||,
filter: filter(P;l),
int_seg: {i..j-},
nat: ℕ,
assert: ↑b,
bool: 𝔹,
less_than: a < 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],
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
es-E-interface: E(X),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
exists: ∃x:A. B[x],
cand: A c∧ B,
int_seg: {i..j-},
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
es-locl: (e <loc e'),
sorted-by: sorted-by(R;L),
less_than: a < b,
es-causl: (e < e'),
squash: ↓T,
sq_stable: SqStable(P)
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}P:E(X) {}\mrightarrow{} \mBbbB{}. \mforall{}n:\mBbbN{}. \mforall{}e:E.
\mexists{}f:\mBbbN{}n {}\mrightarrow{} \{e':E(X)| (\muparrow{}P[e']) \mwedge{} e' \mleq{}loc e \} . \mforall{}i,j:\mBbbN{}n. (f i <loc f j) supposing i < j
supposing n \mleq{} ||filter(\mlambda{}e.P[e];\mleq{}(X)(e))||
Date html generated:
2016_05_17-AM-07_06_37
Last ObjectModification:
2016_01_17-PM-03_07_54
Theory : event-ordering
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