Nuprl Lemma : es-prior-interface-val
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀e:E.
(prior(X)(e) <loc e) ∧ (↑prior(X)(e) ∈b X) ∧ (∀e'':E. ((e'' <loc e) ⇒ (prior(X)(e) <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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
in-eclass: e ∈b X,
es-prior-interface: prior(X),
eclass-val: X(e),
local-pred-class: local-pred-class(P),
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
eclass: EClass(A[eo; e]),
nat: ℕ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
implies: P ⇒ Q,
so_apply: x[s],
or: P ∨ Q,
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
top: Top,
eq_int: (i =z j),
iff: P ⇐⇒ Q,
cand: A c∧ B,
true: True,
not: ¬A,
false: False,
sq_exists: ∃x:{A| B[x]},
exists: ∃x:A. B[x],
rev_implies: P ⇐ Q,
bfalse: ff,
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
es-E-interface: E(X),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T}
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E.
(prior(X)(e) <loc e)
\mwedge{} (\muparrow{}prior(X)(e) \mmember{}\msubb{} X)
\mwedge{} (\mforall{}e'':E. ((e'' <loc e) {}\mRightarrow{} (prior(X)(e) <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_09
Last ObjectModification:
2016_01_17-PM-06_59_34
Theory : event-ordering
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