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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