Nuprl Lemma : p-first-append
∀[A,B:Type]. ∀[L1,L2:(A ⟶ (B + Top)) List].
  (p-first(L1 @ L2) = p-first([p-first(L1); p-first(L2)]) ∈ (A ⟶ (B + Top)))
Proof
Definitions occuring in Statement : 
p-first: p-first(L)
, 
append: as @ bs
, 
cons: [a / b]
, 
nil: []
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
function: x:A ⟶ B[x]
, 
union: left + right
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
p-first: p-first(L)
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
top: Top
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
squash: ↓T
, 
true: True
Lemmas referenced : 
list_accum_append, 
subtype_rel_list, 
top_wf, 
list_accum_cons_lemma, 
list_accum_nil_lemma, 
list_accum_wf, 
equal_wf, 
list_induction, 
all_wf, 
list_wf, 
squash_wf, 
true_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
functionExtensionality, 
hypothesisEquality, 
hypothesis, 
because_Cache, 
sqequalRule, 
sqequalHypSubstitution, 
isect_memberEquality, 
isectElimination, 
thin, 
axiomEquality, 
extract_by_obid, 
applyEquality, 
functionEquality, 
unionEquality, 
independent_isectElimination, 
lambdaEquality, 
voidElimination, 
voidEquality, 
dependent_functionElimination, 
inrEquality, 
equalityTransitivity, 
equalitySymmetry, 
lambdaFormation, 
unionElimination, 
inlEquality, 
independent_functionElimination, 
rename, 
universeEquality, 
imageElimination, 
equalityUniverse, 
levelHypothesis, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed
Latex:
\mforall{}[A,B:Type].  \mforall{}[L1,L2:(A  {}\mrightarrow{}  (B  +  Top))  List].
    (p-first(L1  @  L2)  =  p-first([p-first(L1);  p-first(L2)]))
Date html generated:
2019_10_15-AM-11_08_52
Last ObjectModification:
2018_08_21-PM-01_59_12
Theory : general
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