Nuprl Lemma : es-first-event_wf
∀[es:EO]. ∀[e:E]. ∀[P:{e':E| e' ≤loc e } ⟶ 𝔹].
(es-first-event(es;P;e) ∈ (∃e':{E| (e' ≤loc e ∧ (↑(P e')) ∧ (∀e'':E. ((e'' <loc e') ⇒ (¬↑(P e'')))))})
∨ (↓∀e':E. (e' ≤loc e ⇒ (¬↑(P e')))))
Proof
Definitions occuring in Statement :
es-first-event: es-first-event(es;P;e),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-first-event: es-first-event(es;P;e),
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
sq_exists: ∃x:{A| B[x]},
exists: ∃x:A. B[x],
squash: ↓T,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
less_than: a < b,
rev_implies: P ⇐ Q,
l_member: (x ∈ l),
le: A ≤ B,
less_than': less_than'(a;b),
cand: A c∧ B,
nat: ℕ,
ge: i ≥ j ,
true: True,
uiff: uiff(P;Q)
Latex:
\mforall{}[es:EO]. \mforall{}[e:E]. \mforall{}[P:\{e':E| e' \mleq{}loc e \} {}\mrightarrow{} \mBbbB{}].
(es-first-event(es;P;e) \mmember{} (\mexists{}e':\{E| (e' \mleq{}loc e
\mwedge{} (\muparrow{}(P e'))
\mwedge{} (\mforall{}e'':E. ((e'' <loc e') {}\mRightarrow{} (\mneg{}\muparrow{}(P e'')))))\})
\mvee{} (\mdownarrow{}\mforall{}e':E. (e' \mleq{}loc e {}\mRightarrow{} (\mneg{}\muparrow{}(P e')))))
Date html generated:
2016_05_16-AM-09_39_06
Last ObjectModification:
2016_01_17-PM-01_29_01
Theory : new!event-ordering
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