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: {}
Lemmas :
es-interface-extensionality,
es-prior-match_wf,
es-filter-image_wf,
bool_wf,
eqtt_to_assert,
single-bag_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
empty-bag_wf,
es-interface-pair-prior_wf,
in-eclass_wf,
eclass-val_wf,
es-E_wf,
event-ordering+_subtype,
bag_size_single_lemma,
false_wf,
bag_size_empty_lemma,
es-interface-subtype_rel2,
top_wf,
subtype_top,
es-prior-val_wf,
bag_only_single_lemma,
assert_wf,
eq_int_wf,
bag-size_wf,
bag-only_wf2,
single-valued-bag-single,
eclass_wf,
event-ordering+_wf
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:
2015_07_21-PM-03_49_42
Last ObjectModification:
2015_01_27-PM-06_06_05
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