Nuprl Lemma : member-class-le-before
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].
uiff(v ↓∈ class-le-before(X;es;e);↓∃e':E. (e' ≤loc e ∧ v ∈ X(e')))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
class-le-before: class-le-before(X;es;e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
universe: Type,
bag-member: x ↓∈ bs
Definitions unfolded in proof :
class-le-before: class-le-before(X;es;e),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
so_lambda: λ2x.t[x],
eclass: EClass(A[eo; e]),
so_apply: x[s],
classrel: v ∈ X(e),
squash: ↓T,
exists: ∃x:A. B[x],
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q),
bag-member: x ↓∈ bs,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mdownarrow{}\mmember{} class-le-before(X;es;e);\mdownarrow{}\mexists{}e':E. (e' \mleq{}loc e \mwedge{} v \mmember{} X(e')))
Date html generated:
2016_05_16-PM-01_58_55
Last ObjectModification:
2016_01_17-PM-07_41_08
Theory : event-ordering
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