Nuprl Lemma : decidable__existse-between2
∀es:EO. ∀e1,e2:E.
∀[P:{e:E| loc(e) = loc(e1) ∈ Id} ⟶ ℙ]. ∀e@loc(e1).Dec(P[e]) ⇒ Dec(∃e∈[e1,e2].P[e]) supposing loc(e2) = loc(e1) ∈ Id
Proof
Definitions occuring in Statement :
existse-between2: ∃e∈[e1,e2].P[e],
alle-at: ∀e@i.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uimplies: b supposing a,
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],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
existse-between2: ∃e∈[e1,e2].P[e],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
existse-le: ∃e≤e'.P[e],
and: P ∧ Q,
subtype_rel: A ⊆r B,
alle-at: ∀e@i.P[e],
decidable: Dec(P),
or: P ∨ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
guard: {T},
not: ¬A,
false: False
Latex:
\mforall{}es:EO. \mforall{}e1,e2:E.
\mforall{}[P:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}]
\mforall{}e@loc(e1).Dec(P[e]) {}\mRightarrow{} Dec(\mexists{}e\mmember{}[e1,e2].P[e]) supposing loc(e2) = loc(e1)
Date html generated:
2016_05_16-AM-09_45_31
Last ObjectModification:
2015_12_28-PM-09_40_08
Theory : new!event-ordering
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