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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