Nuprl Lemma : fpf-restrict-dom
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[f:x:A fp-> B[x]]. ∀[P:A ─→ 𝔹]. ∀[x:A].
uiff(↑x ∈ dom(fpf-restrict(f;P));{(↑x ∈ dom(f)) ∧ (↑(P x))})
Proof
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
guard: {T},
so_apply: x[s],
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert_witness,
assert_wf,
bool_wf,
fpf_wf,
deq_wf,
domain_fpf_restrict_lemma,
l_member_wf,
fpf-domain_wf,
subtype-fpf2,
top_wf,
subtype_top,
member_filter,
filter_wf5,
subtype_rel_dep_function,
subtype_rel_self,
set_wf,
iff_wf,
member-fpf-domain,
fpf-restrict_wf2,
fpf-dom_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:x:A fp-> B[x]]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[x:A].
uiff(\muparrow{}x \mmember{} dom(fpf-restrict(f;P));\{(\muparrow{}x \mmember{} dom(f)) \mwedge{} (\muparrow{}(P x))\})
Date html generated:
2015_07_17-AM-11_14_55
Last ObjectModification:
2015_01_28-AM-07_40_08
Home
Index