Nuprl Lemma : fpf-accum_wf
∀[A,C:Type]. ∀[B:A ⟶ Type]. ∀[x:a:A fp-> B[a]]. ∀[y:C]. ∀[f:C ⟶ a:A ⟶ B[a] ⟶ C].
  (fpf-accum(z,a,v.f[z;a;v];y;x) ∈ C)
Proof
Definitions occuring in Statement : 
fpf-accum: fpf-accum(z,a,v.f[z; a; v];y;x)
, 
fpf: a:A fp-> B[a]
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s1;s2;s3]
, 
so_apply: x[s]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
fpf: a:A fp-> B[a]
, 
fpf-accum: fpf-accum(z,a,v.f[z; a; v];y;x)
, 
pi2: snd(t)
, 
pi1: fst(t)
, 
so_apply: x[s]
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2;s3]
, 
so_apply: x[s1;s2]
Lemmas referenced : 
fpf_wf, 
list-subtype, 
list_accum_wf, 
l_member_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
hypothesisEquality, 
applyEquality, 
isect_memberEquality, 
isectElimination, 
because_Cache, 
lemma_by_obid, 
lambdaEquality, 
cumulativity, 
universeEquality, 
setEquality, 
setElimination, 
rename
Latex:
\mforall{}[A,C:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[x:a:A  fp->  B[a]].  \mforall{}[y:C].  \mforall{}[f:C  {}\mrightarrow{}  a:A  {}\mrightarrow{}  B[a]  {}\mrightarrow{}  C].
    (fpf-accum(z,a,v.f[z;a;v];y;x)  \mmember{}  C)
Date html generated:
2018_05_21-PM-09_26_35
Last ObjectModification:
2018_02_09-AM-10_22_00
Theory : finite!partial!functions
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