Nuprl Lemma : es-class-causal-rel-fail_wf
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[f:Id List]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[R:E(X) ⟶ A ⟶ B ⟶ ℙ].
(∀e,x,y. e∈X(x) ⇐c⇒ ∃ Y(y) such that
R[e;x;y]
unless loc(e) ∈ f ∈ ℙ)
Proof
Definitions occuring in Statement :
es-class-causal-rel-fail: es-class-causal-rel-fail,
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2;s3],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
or: P ∨ Q,
exists: ∃x:A. B[x],
so_apply: x[s],
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
guard: {T},
implies: P ⇒ Q,
sq_type: SQType(T),
so_apply: x[s1;s2;s3],
es-E-interface: E(X),
so_lambda: λ2x.t[x],
top: Top,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
es-class-causal-rel-fail: es-class-causal-rel-fail,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:Id List]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[R:E(X)
{}\mrightarrow{} A
{}\mrightarrow{} B
{}\mrightarrow{} \mBbbP{}].
(\mforall{}e,x,y. e\mmember{}X(x) \mLeftarrow{}c\mRightarrow{} \mexists{} Y(y) such that
R[e;x;y]
unless loc(e) \mmember{} f \mmember{} \mBbbP{})
Date html generated:
2016_05_17-AM-08_15_56
Last ObjectModification:
2015_12_28-PM-11_09_46
Theory : event-ordering
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