Nuprl Lemma : prior-val-is
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X:EClass(T)]. ∀[e:E]. ∀[e':E(X)].
({(↑e ∈b (X)') ∧ ((X)'(e) = X(e') ∈ T)}) supposing
((∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑e'' ∈b X))) and
(e' <loc e))
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
es-E-interface: E(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],
guard: {T},
all: ∀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],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
and: P ∧ Q,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
es-E-interface: E(X),
subtype_rel: A ⊆r B,
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
es-locl: (e <loc e'),
or: P ∨ Q,
not: ¬A,
false: False
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[e:E]. \mforall{}[e':E(X)].
(\{(\muparrow{}e \mmember{}\msubb{} (X)') \mwedge{} ((X)'(e) = X(e'))\}) supposing
((\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X))) and
(e' <loc e))
Date html generated:
2016_05_17-AM-06_34_54
Last ObjectModification:
2015_12_29-AM-00_34_34
Theory : event-ordering
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