Nuprl Lemma : es-prior-match-programmable
∀[Info,A,B:Type]. ∀[R:A ⟶ B ⟶ 𝔹]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
(es-prior-match(R; X; Y) = λp.if R (fst(p)) (snd(p)) then {p} else {} fi [X;Y] ∈ EClass(A × B))
Proof
Definitions occuring in Statement :
es-prior-match: es-prior-match(R; X; Y),
es-interface-pair-prior: X;Y,
es-filter-image: f[X],
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
single-bag: {x},
empty-bag: {}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
sv-class: Singlevalued(X),
es-filter-image: f[X],
eclass-compose1: f o X,
eclass-val: X(e),
in-eclass: e ∈b X,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
es-prior-match: es-prior-match(R; X; Y),
band: p ∧b q,
es-interface-pair-prior: X;Y,
eq_int: (i =z j),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
true: True
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[R:A {}\mrightarrow{} B {}\mrightarrow{} \mBbbB{}]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
(es-prior-match(R; X; Y) = \mlambda{}p.if R (fst(p)) (snd(p)) then \{p\} else \{\} fi [X;Y])
Date html generated:
2016_05_17-AM-07_20_16
Last ObjectModification:
2016_01_17-PM-03_05_57
Theory : event-ordering
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