Nuprl Lemma : decidable__existse-before
∀es:EO. ∀e':E. ∀[P:{e:E| loc(e) = loc(e') ∈ Id} ⟶ ℙ]. (∀e@loc(e').Dec(P[e]) ⇒ Dec(∃e<e'.P[e]))
Proof
Definitions occuring in Statement :
existse-before: ∃e<e'.P[e],
alle-at: ∀e@i.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
cand: A c∧ B,
es-E: E,
es-base-E: es-base-E(es),
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
assert: ↑b,
ifthenelse: if b then t else f fi ,
not: ¬A,
true: True,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
bnot: ¬bb,
alle-at: ∀e@i.P[e]
Latex:
\mforall{}es:EO. \mforall{}e':E. \mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]. (\mforall{}e@loc(e').Dec(P[e]) {}\mRightarrow{} Dec(\mexists{}e<e'.P[e]))
Date html generated:
2016_05_16-AM-09_41_25
Last ObjectModification:
2015_12_28-PM-09_43_31
Theory : new!event-ordering
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