Nuprl Lemma : fpf-single_wf2
∀[A,B:Type]. ∀[x:A]. ∀[v:B]. ∀[eqa:EqDecider(A)].  (x : v ∈ a:A fp-> x : B(a)?Top)
Proof
Definitions occuring in Statement : 
fpf-single: x : v
, 
fpf-cap: f(x)?z
, 
fpf: a:A fp-> B[a]
, 
deq: EqDecider(T)
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
fpf-single: x : v
, 
fpf-cap: f(x)?z
, 
all: ∀x:A. B[x]
, 
top: Top
, 
fpf: a:A fp-> B[a]
, 
prop: ℙ
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
ifthenelse: if b then t else f fi 
, 
implies: P 
⇒ Q
, 
bool: 𝔹
Lemmas referenced : 
fpf-single_wf, 
fpf_ap_pair_lemma, 
ifthenelse_wf, 
fpf-dom_wf, 
cons_wf, 
nil_wf, 
l_member_wf, 
top_wf, 
equal_wf, 
deq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
thin, 
instantiate, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
cumulativity, 
hypothesisEquality, 
sqequalRule, 
lambdaEquality, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis, 
dependent_pairEquality, 
functionExtensionality, 
setEquality, 
functionEquality, 
universeEquality, 
because_Cache, 
applyEquality, 
lambdaFormation, 
unionElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
axiomEquality
Latex:
\mforall{}[A,B:Type].  \mforall{}[x:A].  \mforall{}[v:B].  \mforall{}[eqa:EqDecider(A)].    (x  :  v  \mmember{}  a:A  fp->  x  :  B(a)?Top)
Date html generated:
2018_05_21-PM-09_24_27
Last ObjectModification:
2018_05_19-PM-04_36_55
Theory : finite!partial!functions
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