Nuprl Lemma : parallel-classrel-weak
∀[T,Info:Type]. ∀[X,Y:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T]. (v ∈ X || Y(e) ⇐⇒ v ∈ X(e) ↓∨ v ∈ Y(e))
Proof
Definitions occuring in Statement :
parallel-class: X || Y,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
sq_or: a ↓∨ b,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_or: a ↓∨ b,
squash: ↓T,
prop: ℙ,
rev_implies: P ⇐ Q,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs
Latex:
\mforall{}[T,Info:Type]. \mforall{}[X,Y:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
(v \mmember{} X || Y(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} X(e) \mdownarrow{}\mvee{} v \mmember{} Y(e))
Date html generated:
2016_05_16-PM-02_30_42
Last ObjectModification:
2016_01_17-PM-07_31_22
Theory : event-ordering
Home
Index