Nuprl Lemma : decidable__existse-between3
∀es:EO. ∀e1,e2:E.
∀[P:{e:E| (loc(e) = loc(e1) ∈ Id) ∧ (¬↑first(e))} ⟶ ℙ]
∀e@loc(e1).Dec(P[e]) supposing ¬↑first(e) ⇒ Dec(∃e∈(e1,e2].P[e]) supposing loc(e2) = loc(e1) ∈ Id
Proof
Definitions occuring in Statement :
existse-between3: ∃e∈(e1,e2].P[e],
alle-at: ∀e@i.P[e],
es-first: first(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
implies: 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],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
existse-between3: ∃e∈(e1,e2].P[e],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B,
existse-le: ∃e≤e'.P[e],
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
alle-at: ∀e@i.P[e],
decidable: Dec(P),
or: P ∨ Q,
exists: ∃x:A. B[x],
es-locl: (e <loc e'),
guard: {T},
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff
Latex:
\mforall{}es:EO. \mforall{}e1,e2:E.
\mforall{}[P:\{e:E| (loc(e) = loc(e1)) \mwedge{} (\mneg{}\muparrow{}first(e))\} {}\mrightarrow{} \mBbbP{}]
\mforall{}e@loc(e1).Dec(P[e]) supposing \mneg{}\muparrow{}first(e) {}\mRightarrow{} Dec(\mexists{}e\mmember{}(e1,e2].P[e]) supposing loc(e2) = loc(e1)
Date html generated:
2016_05_16-AM-09_46_10
Last ObjectModification:
2015_12_28-PM-09_40_27
Theory : new!event-ordering
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