Nuprl Lemma : first-at-filter-interface-predecessors-or
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X:EClass(T)]. ∀[P:E(X) ⟶ 𝔹]. ∀[Q:E(X) ⟶ ℙ]. ∀[n:ℕ+]. ∀[e:E]. ∀[i:Id].
↑e ∈b X supposing e is first@ i s.t. q.((↑q ∈b X) ∧ Q[q]) ∨ (||filter(λe.P[e];≤(X)(q))|| = n ∈ ℤ)
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first-at: e is first@ i s.t. e.P[e],
es-E: E,
Id: Id,
length: ||as||,
filter: filter(P;l),
nat_plus: ℕ+,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
or: P ∨ Q,
and: P ∧ Q,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
not: ¬A,
false: False,
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
es-E-interface: E(X),
nat_plus: ℕ+,
guard: {T},
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
or: P ∨ Q,
sq_type: SQType(T),
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
bfalse: ff,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
exists: ∃x:A. B[x],
cand: A c∧ B,
es-locl: (e <loc e'),
rev_implies: P ⇐ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[P:E(X) {}\mrightarrow{} \mBbbB{}]. \mforall{}[Q:E(X) {}\mrightarrow{} \mBbbP{}]. \mforall{}[n:\mBbbN{}\msupplus{}].
\mforall{}[e:E]. \mforall{}[i:Id].
\muparrow{}e \mmember{}\msubb{} X supposing e is first@ i s.t. q.((\muparrow{}q \mmember{}\msubb{} X) \mwedge{} Q[q]) \mvee{} (||filter(\mlambda{}e.P[e];\mleq{}(X)(q))|| = n)
Date html generated:
2016_05_17-AM-07_08_27
Last ObjectModification:
2016_01_17-PM-03_04_59
Theory : event-ordering
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