Nuprl Lemma : es-first-at_wf
∀[es:EO]. ∀[i:Id]. ∀[e':E]. ∀[P:{e:E| loc(e) = i ∈ Id} ⟶ ℙ]. (e' is first@ i s.t. e.P[e] ∈ ℙ)
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,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
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,
es-first-at: e is first@ i s.t. e.P[e],
prop: ℙ,
alle-lt: ∀e<e'.P[e],
and: P ∧ Q,
cand: A c∧ B,
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
es-locl: (e <loc e'),
all: ∀x:A. B[x]
Latex:
\mforall{}[es:EO]. \mforall{}[i:Id]. \mforall{}[e':E]. \mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]. (e' is first@ i s.t. e.P[e] \mmember{} \mBbbP{})
Date html generated:
2016_05_16-AM-09_48_49
Last ObjectModification:
2015_12_28-PM-09_35_58
Theory : new!event-ordering
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