Nuprl Lemma : es-prior-interface-same
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)].
(∀[e:E]. uiff(↑e ∈b prior(X);↑e ∈b prior(Y))) ∧ (∀[e:E]. prior(Y)(e) = prior(X)(e) ∈ E supposing ↑e ∈b prior(X))
supposing ∀e:E. (↑e ∈b X ⇐⇒ ↑e ∈b 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-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
es-E-interface: E(X),
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
(\mforall{}[e:E]. uiff(\muparrow{}e \mmember{}\msubb{} prior(X);\muparrow{}e \mmember{}\msubb{} prior(Y)))
\mwedge{} (\mforall{}[e:E]. prior(Y)(e) = prior(X)(e) supposing \muparrow{}e \mmember{}\msubb{} prior(X))
supposing \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \muparrow{}e \mmember{}\msubb{} Y)
Date html generated:
2016_05_16-PM-11_55_27
Last ObjectModification:
2015_12_29-AM-01_03_32
Theory : event-ordering
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