Nuprl Lemma : fpf-type
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:a:A fp-> B[a]].  (f ∈ a:{a:A| (a ∈ fpf-domain(f))}  fp-> B[a])
Proof
Definitions occuring in Statement : 
fpf-domain: fpf-domain(f)
, 
fpf: a:A fp-> B[a]
, 
l_member: (x ∈ l)
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
fpf: a:A fp-> B[a]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
fpf-domain: fpf-domain(f)
, 
pi1: fst(t)
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
Lemmas referenced : 
fpf_wf, 
list-subtype, 
subtype_rel_dep_function, 
l_member_wf, 
set_wf, 
subtype_rel_self
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
hypothesis, 
sqequalRule, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
lemma_by_obid, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaEquality, 
applyEquality, 
isect_memberEquality, 
because_Cache, 
functionEquality, 
cumulativity, 
universeEquality, 
productElimination, 
dependent_pairEquality, 
setEquality, 
setElimination, 
rename, 
lambdaFormation, 
dependent_set_memberEquality, 
independent_isectElimination
Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[f:a:A  fp->  B[a]].    (f  \mmember{}  a:\{a:A|  (a  \mmember{}  fpf-domain(f))\}    fp->  B[a])
Date html generated:
2018_05_21-PM-09_17_28
Last ObjectModification:
2018_02_09-AM-10_16_31
Theory : finite!partial!functions
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