Nuprl Lemma : interface-union-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 inl X(e) else inr Y(e) fi ∈ (A + B) supposing ↑e ∈b X+Y
Proof
Definitions occuring in Statement :
es-interface-union: 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],
inr: inr x ,
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T
Lemmas :
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,
bag-only_wf2,
single-valued-bag-if-le1,
le_weakening,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
bag_size_empty_lemma,
false_wf,
assert_wf,
in-eclass_wf,
es-interface-union_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
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 inl X(e) else inr Y(e) fi supposing \muparrow{}e \mmember{}\msubb{} X+Y
Date html generated:
2015_07_20-PM-03_19_42
Last ObjectModification:
2015_01_27-PM-10_23_32
Home
Index