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
Lemmas :
subtype-fpf3,
top_wf,
strong-subtype-set2,
subtype_rel_self,
set_wf,
list_wf,
l_member_wf
\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:
2015_07_17-AM-09_15_46
Last ObjectModification:
2015_01_28-AM-07_53_37
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