Nuprl Lemma : fpf-restrict_wf
∀[A:Type]. ∀[B:A ─→ Type]. ∀[f:x:A fp-> B[x]]. ∀[P:A ─→ 𝔹]. (fpf-restrict(f;P) ∈ x:{x:A| ↑(P x)} fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf: a:A fp-> B[a],
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
filter_type,
assert_wf,
l_member_wf,
set_wf,
bool_wf,
fpf_wf,
subtype_rel_dep_function,
subtype_rel_self,
l_member-settype,
member_filter
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:x:A fp-> B[x]]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. (fpf-restrict(f;P) \mmember{} x:\{x:A| \muparrow{}(P x)\} f\000Cp-> B[x])
Date html generated:
2015_07_17-AM-11_14_39
Last ObjectModification:
2015_01_28-AM-07_40_45
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