Nuprl Lemma : pairs-fpf_wf
∀[A,B:Type]. ∀[eq1:EqDecider(A)]. ∀[eq2:EqDecider(B)]. ∀[L:(A × B) List].  (fpf(L) ∈ a:A fp-> B List)
Proof
Definitions occuring in Statement : 
pairs-fpf: fpf(L)
, 
fpf: a:A fp-> B[a]
, 
list: T List
, 
deq: EqDecider(T)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
product: x:A × B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
pairs-fpf: fpf(L)
, 
fpf: a:A fp-> B[a]
, 
eqof: eqof(d)
, 
top: Top
, 
all: ∀x:A. B[x]
, 
prop: ℙ
, 
deq: EqDecider(T)
, 
pi1: fst(t)
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
pi2: snd(t)
, 
bfalse: ff
Lemmas referenced : 
remove-repeats_wf, 
map_wf, 
pi1_wf_top, 
l_member_wf, 
reduce_wf, 
list_wf, 
bool_wf, 
eqtt_to_assert, 
safe-assert-deq, 
insert_wf, 
equal_wf, 
nil_wf, 
deq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
dependent_pairEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
productEquality, 
lambdaEquality, 
productElimination, 
independent_pairEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis, 
lambdaFormation, 
setElimination, 
rename, 
because_Cache, 
applyEquality, 
sqequalRule, 
unionElimination, 
equalityElimination, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
setEquality, 
functionEquality, 
axiomEquality, 
universeEquality
Latex:
\mforall{}[A,B:Type].  \mforall{}[eq1:EqDecider(A)].  \mforall{}[eq2:EqDecider(B)].  \mforall{}[L:(A  \mtimes{}  B)  List].
    (fpf(L)  \mmember{}  a:A  fp->  B  List)
Date html generated:
2018_05_21-PM-09_31_51
Last ObjectModification:
2018_02_09-AM-10_26_44
Theory : finite!partial!functions
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