Nuprl Lemma : es-le-before-filter
∀es:EO. ∀e,b:E. (b ≤loc e ⇒ (≤loc(b) = filter(λa.a ≤loc b;≤loc(e)) ∈ ({a:E| a ≤loc b } List)))
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-ble: e ≤loc e',
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
filter: filter(P;l),
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
lambda: λx.A[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
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},
subtype_rel: A ⊆r B,
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,
iff: P ⇐⇒ Q,
cand: A c∧ B,
true: True,
es-le-before: ≤loc(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
so_apply: x[s],
so_lambda: λ2x.t[x]
Latex:
\mforall{}es:EO. \mforall{}e,b:E. (b \mleq{}loc e {}\mRightarrow{} (\mleq{}loc(b) = filter(\mlambda{}a.a \mleq{}loc b;\mleq{}loc(e))))
Date html generated:
2016_05_16-AM-09_34_58
Last ObjectModification:
2016_01_17-PM-01_33_42
Theory : new!event-ordering
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