Nuprl Lemma : assert-eo-forward-first
∀[Info:Type]. ∀eo:EO+(Info). ∀e:E. ∀e':E. uiff(↑first(e');(e' = e ∈ E) ∨ ((¬(loc(e') = loc(e) ∈ Id)) ∧ (↑first(e'))))
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-first: first(e),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
assert: ↑b,
true: True,
or: P ∨ Q,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
cand: A c∧ B,
top: Top
Latex:
\mforall{}[Info:Type]
\mforall{}eo:EO+(Info). \mforall{}e:E. \mforall{}e':E. uiff(\muparrow{}first(e');(e' = e) \mvee{} ((\mneg{}(loc(e') = loc(e))) \mwedge{} (\muparrow{}first(e'))))
Date html generated:
2016_05_16-PM-01_10_46
Last ObjectModification:
2015_12_29-PM-01_52_08
Theory : event-ordering
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