Nuprl Lemma : eo-forward-first-trivial
∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e,e':E]. first(e) ~ tt supposing e' = e ∈ E
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-first: first(e),
es-E: E,
btrue: tt,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
iff: P ⇐⇒ Q,
true: True,
rev_implies: P ⇐ Q,
assert: ↑b,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
not: ¬A
Latex:
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e,e':E]. first(e) \msim{} tt supposing e' = e
Date html generated:
2016_05_16-PM-01_08_37
Last ObjectModification:
2015_12_29-PM-01_49_57
Theory : event-ordering
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