Nuprl Lemma : prior-val-val
∀[Info:Type]
∀es:EO+(Info)
∀[T:Type]
∀X:EClass(T). ∀e:E.
∃e':E
((e' <loc e) ∧ (↑e' ∈b X) ∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑e'' ∈b X))) ∧ ((X)'(e) = X(e') ∈ T))
supposing ↑e ∈b (X)'
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
es-prior-val: (X)',
eclass-val: X(e),
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
es-E-interface: E(X),
cand: A c∧ B,
not: ¬A,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}e:E.
\mexists{}e':E
((e' <loc e)
\mwedge{} (\muparrow{}e' \mmember{}\msubb{} X)
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X)))
\mwedge{} ((X)'(e) = X(e')))
supposing \muparrow{}e \mmember{}\msubb{} (X)'
Date html generated:
2016_05_17-AM-06_34_37
Last ObjectModification:
2015_12_29-AM-00_32_40
Theory : event-ordering
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