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),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
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,
pi2: snd(t),
bfalse: ff
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:
2016_05_16-AM-11_36_41
Last ObjectModification:
2015_12_29-AM-09_31_33
Theory : event-ordering
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