Nuprl Lemma : es-local-pred_wf2
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[P:{e':E| (e' <loc e)} ⟶ 𝔹].
(last(P) e ∈ (∃e':{E| ((e' <loc e) ∧ (↑(P e')) ∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑(P e'')))))})
∨ (¬(∃e':{E| ((e' <loc e) ∧ (↑(P e')))})))
Proof
Definitions occuring in Statement :
es-local-pred: last(P),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
not: ¬A,
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],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-local-pred: last(P),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_exists: ∃x:{A| B[x]},
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
cand: A c∧ B,
iff: P ⇐⇒ Q,
true: True,
rev_implies: P ⇐ Q,
label: ...$L... t
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[P:\{e':E| (e' <loc e)\} {}\mrightarrow{} \mBbbB{}].
(last(P) e \mmember{} (\mexists{}e':\{E| ((e' <loc e)
\mwedge{} (\muparrow{}(P e'))
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}(P e'')))))\})
\mvee{} (\mneg{}(\mexists{}e':\{E| ((e' <loc e) \mwedge{} (\muparrow{}(P e')))\})))
Date html generated:
2016_05_16-PM-11_18_13
Last ObjectModification:
2016_01_17-PM-07_27_54
Theory : event-ordering
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