Nuprl Lemma : es-interface-val-conditional
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X,Y:EClass(A)]. ∀[e:E].
[X?Y](e) = if e ∈b X then X(e) else Y(e) fi ∈ A supposing ↑e ∈b [X?Y]
Proof
Definitions occuring in Statement :
cond-class: [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],
universe: Type,
equal: s = t ∈ T
Lemmas :
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
bool_wf,
eqtt_to_assert,
bag-only_wf2,
single-valued-bag-if-le1,
le_weakening,
decidable__lt,
bag-size_wf,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
equal-wf-T-base,
iff_weakening_uiff,
assert_of_eq_int,
assert_wf,
member_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
eclass_wf,
event-ordering+_wf,
cond-class_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X,Y:EClass(A)]. \mforall{}[e:E].
[X?Y](e) = if e \mmember{}\msubb{} X then X(e) else Y(e) fi supposing \muparrow{}e \mmember{}\msubb{} [X?Y]
Date html generated:
2015_07_20-PM-03_17_18
Last ObjectModification:
2015_01_27-PM-10_35_10
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