Nuprl Lemma : cond-class-val
∀[Info,A:Type]. ∀[X,Y:EClass(A)]. ∀[es:EO+(Info)]. ∀[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 :
eq_int_wf,
bag-size_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf,
assert_wf,
in-eclass_wf,
cond-class_wf,
top_wf,
dep-eclass_subtype_rel,
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,
not-equal-2,
true_wf
\mforall{}[Info,A:Type]. \mforall{}[X,Y:EClass(A)]. \mforall{}[es:EO+(Info)]. \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_17-PM-00_47_37
Last ObjectModification:
2015_01_27-PM-11_06_19
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