Nuprl Lemma : es-prior-interface-equal
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. ∀[e:E].
(prior(X)(e) = prior(Y)(e) ∈ E) supposing
((∀e':E. (((prior(X)(e) <loc e') ∨ (prior(Y)(e) <loc e')) ⇒ (e' <loc e) ⇒ (↑e' ∈b X ⇐⇒ ↑e' ∈b Y))) and
(↑e ∈b prior(X)) and
(↑e ∈b prior(Y)))
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-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
es-E-interface: E(X),
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
es-locl: (e <loc e'),
not: ¬A,
false: False,
guard: {T}
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)]. \mforall{}[e:E].
(prior(X)(e) = prior(Y)(e)) supposing
((\mforall{}e':E
(((prior(X)(e) <loc e') \mvee{} (prior(Y)(e) <loc e'))
{}\mRightarrow{} (e' <loc e)
{}\mRightarrow{} (\muparrow{}e' \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \muparrow{}e' \mmember{}\msubb{} Y))) and
(\muparrow{}e \mmember{}\msubb{} prior(X)) and
(\muparrow{}e \mmember{}\msubb{} prior(Y)))
Date html generated:
2016_05_16-PM-11_55_08
Last ObjectModification:
2015_12_29-AM-01_01_44
Theory : event-ordering
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