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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
rev_implies: P ⇐ Q,
top: Top
Latex:
\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:
2016_05_16-AM-11_33_44
Last ObjectModification:
2015_12_29-AM-09_29_16
Theory : event-ordering
Home
Index