Nuprl Lemma : decidable__exists-last-classrel-between3
∀[Info,T:Type].
∀X:EClass(T). ∀es:EO+(Info). ∀e1,e2:E.
Dec(∃e:E
((e1 <loc e)
∧ e ≤loc e2
∧ (↓∃v:T. v ∈ X(e))
∧ (∀e'':E. ((e <loc e'') ⇒ e'' ≤loc e2 ⇒ (∀x:T. (¬x ∈ X(e'')))))))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
guard: {T},
nat: ℕ,
prop: ℙ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
cand: A c∧ B,
es-E: E,
es-base-E: es-base-E(es),
rev_implies: P ⇐ Q,
es-le: e ≤loc e' ,
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
es-locl: (e <loc e'),
label: ...$L... t
Latex:
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e1,e2:E.
Dec(\mexists{}e:E
((e1 <loc e)
\mwedge{} e \mleq{}loc e2
\mwedge{} (\mdownarrow{}\mexists{}v:T. v \mmember{} X(e))
\mwedge{} (\mforall{}e'':E. ((e <loc e'') {}\mRightarrow{} e'' \mleq{}loc e2 {}\mRightarrow{} (\mforall{}x:T. (\mneg{}x \mmember{} X(e'')))))))
Date html generated:
2016_05_16-PM-01_40_10
Last ObjectModification:
2016_01_17-PM-07_59_51
Theory : event-ordering
Home
Index