Nuprl Lemma : es-prior-interface-val-pred
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
prior(X)(e) = if pred(e) ∈b X then pred(e) else prior(X)(pred(e)) fi ∈ E supposing ↑e ∈b prior(X)
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-pred: pred(e),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
es-E-interface: E(X),
or: P ∨ Q,
not: ¬A,
false: False,
decidable: Dec(P),
guard: {T},
es-locl: (e <loc e')
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
prior(X)(e) = if pred(e) \mmember{}\msubb{} X then pred(e) else prior(X)(pred(e)) fi supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2016_05_16-PM-11_56_43
Last ObjectModification:
2015_12_29-AM-01_04_45
Theory : event-ordering
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