Nuprl Lemma : fpf-trivial-subtype-set
∀[A:Type]. ∀[P:A ⟶ ℙ]. ∀[f:a:{a:A| P[a]} fp-> Type × Top]. (f ∈ a:A fp-> Type × Top)
Proof
Definitions occuring in Statement :
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ,
fpf: a:A fp-> B[a]
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:a:\{a:A| P[a]\} fp-> Type \mtimes{} Top]. (f \mmember{} a:A fp-> Type \mtimes{} Top)
Date html generated:
2016_05_16-AM-11_03_42
Last ObjectModification:
2015_12_29-AM-09_15_27
Theory : event-ordering
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