Nuprl Lemma : prior-class-when-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. ∀[d:Top]. ∀[e:E].
(X'?d) when Y(e) ~ <Y(e), if e ∈b (X)' then (X)'(e) else d fi > supposing ↑e ∈b (X'?d) when Y
Proof
Definitions occuring in Statement :
es-prior-class-when: (X'?d) when Y,
es-prior-val: (X)',
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
pair: <a, b>,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
es-prior-class-when: (X'?d) when Y,
in-eclass: e ∈b X,
eclass-val: X(e),
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
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 ,
top: Top,
eq_int: (i =z j),
assert: ↑b,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)]. \mforall{}[d:Top]. \mforall{}[e:E].
(X'?d) when Y(e) \msim{} <Y(e), if e \mmember{}\msubb{} (X)' then (X)'(e) else d fi > supposing \muparrow{}e \mmember{}\msubb{} (X'?d) when Y
Date html generated:
2016_05_17-AM-07_19_24
Last ObjectModification:
2015_12_28-PM-11_58_17
Theory : event-ordering
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