Nuprl Lemma : es-local-le-pred_wf
∀[Info:Type]. ∀[P:es:EO+(Info) ⟶ E ⟶ 𝔹]. (≤(P) ∈ EClass({e:E| ↑(P es e)} ))
Proof
Definitions occuring in Statement :
es-local-le-pred: ≤(P),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
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,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
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,
prop: ℙ,
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-le-pred: ≤(P),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
eclass: EClass(A[eo; e])
Latex:
\mforall{}[Info:Type]. \mforall{}[P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbB{}]. (\mleq{}(P) \mmember{} EClass(\{e:E| \muparrow{}(P es e)\} ))
Date html generated:
2016_05_16-PM-11_29_25
Last ObjectModification:
2016_01_17-PM-07_12_07
Theory : event-ordering
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