Nuprl Lemma : fpf-null-domain
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:Void ⟶ Top].  (<[], f> = ⊗ ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement : 
fpf-empty: ⊗
, 
fpf: a:A fp-> B[a]
, 
nil: []
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
so_apply: x[s]
, 
function: x:A ⟶ B[x]
, 
pair: <a, b>
, 
void: Void
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
fpf-empty: ⊗
, 
fpf: a:A fp-> B[a]
, 
uimplies: b supposing a
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
prop: ℙ
, 
so_apply: x[s]
Lemmas referenced : 
nil_wf, 
null_nil_lemma, 
btrue_wf, 
member-implies-null-eq-bfalse, 
btrue_neq_bfalse, 
l_member_wf, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
dependent_pairEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
functionExtensionality, 
sqequalRule, 
setElimination, 
rename, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
voidElimination, 
setEquality, 
functionEquality, 
applyEquality, 
voidEquality, 
isect_memberEquality, 
axiomEquality, 
because_Cache, 
cumulativity, 
universeEquality
Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[f:Void  {}\mrightarrow{}  Top].    (<[],  f>  =  \motimes{})
Date html generated:
2018_05_21-PM-09_17_45
Last ObjectModification:
2018_02_09-AM-10_16_43
Theory : finite!partial!functions
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