Nuprl Lemma : es-first-at-unique
∀[es:EO]. ∀[i:Id]. ∀[P:{e:E| loc(e) = i ∈ Id} ⟶ ℙ]. ∀[e1,e2:E].
(e1 = e2 ∈ E) supposing (e2 is first@ i s.t. e.P[e] and e1 is first@ i s.t. e.P[e])
Proof
Definitions occuring in Statement :
es-first-at: e is first@ i s.t. e.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-first-at: e is first@ i s.t. e.P[e],
and: P ∧ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
alle-lt: ∀e<e'.P[e],
implies: P ⇒ Q,
not: ¬A,
false: False
Latex:
\mforall{}[es:EO]. \mforall{}[i:Id]. \mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]. \mforall{}[e1,e2:E].
(e1 = e2) supposing (e2 is first@ i s.t. e.P[e] and e1 is first@ i s.t. e.P[e])
Date html generated:
2016_05_16-AM-09_49_18
Last ObjectModification:
2015_12_28-PM-09_35_52
Theory : new!event-ordering
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