Nuprl Lemma : interface-or-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[e:E].
(X | Y)(e)
= if e ∈b X then if e ∈b Y then oobboth(<X(e), Y(e)>) else oobleft(X(e)) fi else oobright(Y(e)) fi
∈ one_or_both(A;B)
supposing ↑e ∈b (X | Y)
Proof
Definitions occuring in Statement :
es-interface-or: (X | Y),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pair: <a, b>,
universe: Type,
equal: s = t ∈ T,
oobright: oobright(rval),
oobleft: oobleft(lval),
oobboth: oobboth(bval),
one_or_both: one_or_both(A;B)
Lemmas :
bag_wf,
eq_int_wf,
bag-size_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_wf,
bag_size_single_lemma,
bag_only_single_lemma,
oobboth_wf,
bag-only_wf2,
single-valued-bag-if-le1,
le_weakening,
decidable__lt,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
add-commutes,
zero-add,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
oobleft_wf,
not-equal-2,
oobright_wf,
bag_size_empty_lemma,
assert_wf,
in-eclass_wf,
es-interface-or_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
one_or_both_wf,
eclass_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[e:E].
(X | Y)(e)
= if e \mmember{}\msubb{} X then if e \mmember{}\msubb{} Y then oobboth(<X(e), Y(e)>) else oobleft(X(e)) fi else oobright(Y(e)) f\000Ci
supposing \muparrow{}e \mmember{}\msubb{} (X | Y)
Date html generated:
2015_07_20-PM-03_24_13
Last ObjectModification:
2015_01_27-PM-10_23_57
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