Nuprl Lemma : es-fset-at-loc
∀es:EO. ∀i:Id. ∀s:fset(E).
∃L:E List. ((∀e:E. (e ∈ s ∧ (loc(e) = i ∈ Id) ⇐⇒ (e ∈ L))) ∧ no_repeats(E;L) ∧ sorted-by(λe,e'. e ≤loc e' ;L))
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-eq: es-eq(es),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
fset-member: a ∈ s,
fset: fset(T),
Id: Id,
sorted-by: sorted-by(R;L),
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
list: T List,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
lambda: λx.A[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T},
rev_uimplies: rev_uimplies(P;Q),
l_contains: A ⊆ B,
l_member: (x ∈ l),
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top
Latex:
\mforall{}es:EO. \mforall{}i:Id. \mforall{}s:fset(E).
\mexists{}L:E List
((\mforall{}e:E. (e \mmember{} s \mwedge{} (loc(e) = i) \mLeftarrow{}{}\mRightarrow{} (e \mmember{} L))) \mwedge{} no\_repeats(E;L) \mwedge{} sorted-by(\mlambda{}e,e'. e \mleq{}loc e' ;L))
Date html generated:
2016_05_16-AM-10_12_53
Last ObjectModification:
2016_01_17-PM-01_21_42
Theory : new!event-ordering
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