Nuprl Lemma : last-decidable
∀es:EO. ∀e:E.
∀[P:{a:E| loc(a) = loc(e) ∈ Id} ⟶ ℙ]
((∀a:{a:E| loc(a) = loc(e) ∈ Id} . Dec(P[a]))
⇒ (∀e'≤e.P[e'] ⇐⇒ P[e] ∨ ∃e'≤e.(¬(P[e'] ⇐⇒ P[e])) ∧ ∀e''∈(e',e].P[e''] ⇐⇒ P[e]))
Proof
Definitions occuring in Statement :
alle-between3: ∀e∈(e1,e2].P[e],
alle-le: ∀e≤e'.P[e],
existse-le: ∃e≤e'.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],
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: 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],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
guard: {T},
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
true: True,
alle-between3: ∀e∈(e1,e2].P[e],
existse-le: ∃e≤e'.P[e],
alle-le: ∀e≤e'.P[e],
cand: A c∧ B,
es-locl: (e <loc e')
Latex:
\mforall{}es:EO. \mforall{}e:E.
\mforall{}[P:\{a:E| loc(a) = loc(e)\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}a:\{a:E| loc(a) = loc(e)\} . Dec(P[a]))
{}\mRightarrow{} (\mforall{}e'\mleq{}e.P[e'] \mLeftarrow{}{}\mRightarrow{} P[e] \mvee{} \mexists{}e'\mleq{}e.(\mneg{}(P[e'] \mLeftarrow{}{}\mRightarrow{} P[e])) \mwedge{} \mforall{}e''\mmember{}(e',e].P[e''] \mLeftarrow{}{}\mRightarrow{} P[e]))
Date html generated:
2016_05_16-AM-09_51_09
Last ObjectModification:
2015_12_28-PM-09_38_49
Theory : new!event-ordering
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