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]
Lemmas referenced : 
subtype-fpf3, 
top_wf, 
strong-subtype-set2, 
subtype_rel_self, 
set_wf, 
l_member_wf, 
list_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
hypothesisEquality, 
applyEquality, 
thin, 
instantiate, 
extract_by_obid, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
cumulativity, 
setEquality, 
because_Cache, 
sqequalRule, 
lambdaEquality, 
productEquality, 
universeEquality, 
independent_isectElimination, 
lambdaFormation, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality
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:
2019_10_16-AM-11_25_09
Last ObjectModification:
2018_08_22-AM-09_57_31
Theory : finite!partial!functions
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