Nuprl Lemma : eo-forward-trivial
∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e:E]. eo.e = eo ∈ EO+(Info) supposing ↑first(e)
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-first: first(e),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
eo-forward: eo.e,
eo-restrict: eo-restrict(eo;P),
es-dom: es-dom(es),
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
es-E: E,
es-base-E: es-base-E(es),
iff: P ⇐⇒ Q,
bor: p ∨bq,
not: ¬A,
rev_implies: P ⇐ Q,
es-le: e ≤loc e' ,
true: True,
event-ordering+: EO+(Info),
event_ordering: EO,
record+: record+,
record-select: r.x,
top: Top,
eq_atom: x =a y,
record-update: r[x := v],
eo_record: eo_record{i:l}(),
so_lambda: λ2x.t[x],
so_apply: x[s],
eo_axioms: eo_axioms(r),
eo-record-type: eo-record-type{i:l}(r),
sq_stable: SqStable(P),
squash: ↓T,
eo-reset-dom: eo-reset-dom(es;d)
Latex:
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e:E]. eo.e = eo supposing \muparrow{}first(e)
Date html generated:
2016_05_16-PM-01_09_49
Last ObjectModification:
2016_01_17-PM-08_01_30
Theory : event-ordering
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