Nuprl Lemma : prior-classrel-p-local-pred
∀[T,Info:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].
uiff(v ∈ Prior(X)(e);↓∃e':E. ((es-p-local-pred(es;λe'.(↓∃w:T. w ∈ X(e'))) e e') ∧ v ∈ X(e')))
Proof
Definitions occuring in Statement :
primed-class: Prior(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-local-pred: es-p-local-pred(es;P),
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
lambda: λx.A[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
eclass: EClass(A[eo; e]),
or: P ∨ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
top: Top,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
inhabited-classrel: inhabited-classrel(eo;T;X;e)
Latex:
\mforall{}[T,Info:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mmember{} Prior(X)(e);\mdownarrow{}\mexists{}e':E. ((es-p-local-pred(es;\mlambda{}e'.(\mdownarrow{}\mexists{}w:T. w \mmember{} X(e'))) e e') \mwedge{} v \mmember{} X(e')))
Date html generated:
2016_05_17-AM-09_27_23
Last ObjectModification:
2016_01_17-PM-11_10_53
Theory : classrel!lemmas
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