Nuprl Lemma : es-interface-pair-prior-programmable
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
X;Y
= eclass-compose2(λys,xs. if (#(ys) =z 1)
then if (#(xs) =z 1) then {<only(xs), only(ys)>} else {} fi
else {}
fi ;Y;Prior(X))
∈ EClass(A × B)
supposing Singlevalued(X)
Proof
Definitions occuring in Statement :
es-interface-pair-prior: X;Y,
primed-class: Prior(X),
eclass-compose2: eclass-compose2(f;X;Y),
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-only: only(bs),
bag-size: #(bs),
single-bag: {x},
empty-bag: {}
Lemmas :
bag-size-one,
equal_wf,
bag-only_wf2,
single-valued-bag-if-le1,
le_weakening,
decidable__lt,
bag-size_wf,
nat_wf,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel,
bag-member-single,
bag-member_wf,
single-bag_wf,
add-zero,
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
bool_wf,
eqtt_to_assert,
bag_size_single_lemma,
assert_functionality_wrt_uiff,
primed-class-prior-val,
true_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
bag_size_empty_lemma,
es-prior-val_wf,
is-pair-prior,
es-interface-pair-prior_wf,
subtype_top,
iff_wf,
eclass-compose2_wf,
eq_int_wf,
assert_of_eq_int,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
empty-bag_wf,
bag_wf,
primed-class_wf,
bag_only_single_lemma,
eclass-val_wf,
squash_wf,
eclass_wf,
event-ordering+_cumulative2,
iff_weakening_equal
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
X;Y
= eclass-compose2(\mlambda{}ys,xs. if (\#(ys) =\msubz{} 1)
then if (\#(xs) =\msubz{} 1) then \{<only(xs), only(ys)>\} else \{\} fi
else \{\}
fi ;Y;Prior(X))
supposing Singlevalued(X)
Date html generated:
2015_07_21-PM-03_48_05
Last ObjectModification:
2015_02_04-PM-06_12_49
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