Nuprl Lemma : es-first-at-since'_wf
∀[es:EO]. ∀[i:Id]. ∀[e':E]. ∀[P,R:{e:E| loc(e) = i ∈ Id} ⟶ ℙ]. (es-first-at-since'(es;i;e';e.R[e];e.P[e]) ∈ ℙ)
Proof
Definitions occuring in Statement :
es-first-at-since': es-first-at-since'(es;i;e;e.R[e];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-since': es-first-at-since'(es;i;e;e.R[e];e.P[e]),
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
es-locl: (e <loc e'),
implies: P ⇒ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Latex:
\mforall{}[es:EO]. \mforall{}[i:Id]. \mforall{}[e':E]. \mforall{}[P,R:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}].
(es-first-at-since'(es;i;e';e.R[e];e.P[e]) \mmember{} \mBbbP{})
Date html generated:
2016_05_16-AM-09_49_58
Last ObjectModification:
2015_12_28-PM-09_35_45
Theory : new!event-ordering
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