Nuprl Lemma : es-prior-interface-val-unique
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
∀[p:E]
p = prior(X)(e) ∈ E supposing (p <loc e) ∧ (↑p ∈b X) ∧ (∀e'':E. ((e'' <loc e) ⇒ (p <loc e'') ⇒ (¬↑e'' ∈b X)))
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-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],
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,
uimplies: b supposing a,
and: P ∧ Q,
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-E-interface: E(X),
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False,
es-locl: (e <loc e')
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
\mforall{}[p:E]
p = prior(X)(e)
supposing (p <loc e) \mwedge{} (\muparrow{}p \mmember{}\msubb{} X) \mwedge{} (\mforall{}e'':E. ((e'' <loc e) {}\mRightarrow{} (p <loc e'') {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X)))
supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2016_05_16-PM-11_54_31
Last ObjectModification:
2015_12_29-AM-01_03_49
Theory : event-ordering
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