Nuprl Lemma : fpf-restrict_wf2
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:x:A fp-> B[x]]. ∀[P:A ⟶ 𝔹]. (fpf-restrict(f;P) ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf: a:A fp-> B[a],
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-restrict: fpf-restrict(f;P),
fpf: a:A fp-> B[a],
fpf-domain: fpf-domain(f),
mk_fpf: mk_fpf(L;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi1: fst(t),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
pi2: snd(t),
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q
Latex:
\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:A fp-> B[x])
Date html generated:
2016_05_16-AM-11_33_19
Last ObjectModification:
2015_12_29-AM-09_28_54
Theory : event-ordering
Home
Index