Nuprl Lemma : es-first-at-exists2
∀es:EO. ∀i:Id.
∀[P:{e:E| loc(e) = i ∈ Id} ⟶ ℙ]
((∀e:{e:E| loc(e) = i ∈ Id} . Dec(P[e]))
⇒ (∀e:E. (∃e'≤e.e' is first@ i s.t. e'.P[e']) supposing ((¬∀e'≤e.¬P[e']) and (loc(e) = i ∈ Id))))
Proof
Definitions occuring in Statement :
es-first-at: e is first@ i s.t. e.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),
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,
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,
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B,
alle-at: ∀e@i.P[e],
decidable: Dec(P),
or: P ∨ Q,
existse-le: ∃e≤e'.P[e],
exists: ∃x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
guard: {T},
alle-le: ∀e≤e'.P[e]
Latex:
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:\{e:E| loc(e) = i\} . Dec(P[e]))
{}\mRightarrow{} (\mforall{}e:E. (\mexists{}e'\mleq{}e.e' is first@ i s.t. e'.P[e']) supposing ((\mneg{}\mforall{}e'\mleq{}e.\mneg{}P[e']) and (loc(e) = i))))
Date html generated:
2016_05_16-AM-09_49_04
Last ObjectModification:
2015_12_28-PM-09_36_48
Theory : new!event-ordering
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