Nuprl Lemma : local-class-output-agree
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[P:LocalClass(X)]. ∀[eo1,eo2:EO+(Info)]. ∀[e1:E]. ∀[e2:E].
(X(e1) = X(e2) ∈ bag(A)) supposing (eo-local-agree(Info;eo1;eo2;e1;e2) and (loc(e1) = loc(e2) ∈ Id))
Proof
Definitions occuring in Statement :
eo-local-agree: eo-local-agree(Info;eo1;eo2;e1;e2),
local-class: LocalClass(X),
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
all: ∀x:A. B[x],
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
Id: Id,
sq_type: SQType(T),
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
eo-local-agree: eo-local-agree(Info;eo1;eo2;e1;e2),
es-le-before: ≤loc(e),
top: Top,
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
true: True,
ge: i ≥ j
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[P:LocalClass(X)]. \mforall{}[eo1,eo2:EO+(Info)]. \mforall{}[e1:E]. \mforall{}[e2:E].
(X(e1) = X(e2)) supposing (eo-local-agree(Info;eo1;eo2;e1;e2) and (loc(e1) = loc(e2)))
Date html generated:
2016_05_16-PM-02_06_35
Last ObjectModification:
2016_01_17-PM-07_40_54
Theory : event-ordering
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