Nuprl Lemma : mapfilter-class_wf
∀[Info,A,B:Type]. ∀[P:A ─→ 𝔹]. ∀[f:A ─→ B]. ∀[X:EClass(A)]. ((f[v] where v from X such that P[v]) ∈ EClass(B))
Proof
Definitions occuring in Statement :
mapfilter-class: (f[v] where v from X such that P[v]),
eclass: EClass(A[eo; e]),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-filter-image_wf,
bool_wf,
eqtt_to_assert,
single-bag_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
empty-bag_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf
\mforall{}[Info,A,B:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[X:EClass(A)].
((f[v] where v from X such that P[v]) \mmember{} EClass(B))
Date html generated:
2015_07_17-PM-01_07_19
Last ObjectModification:
2015_01_27-PM-10_33_13
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