Nuprl Lemma : length-concat
∀[ll:Top List List]. (||concat(ll)|| = l_sum(map(λl.||l||;ll)) ∈ ℤ)
Proof
Definitions occuring in Statement :
l_sum: l_sum(L),
length: ||as||,
concat: concat(ll),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
l_sum: l_sum(L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
implies: P ⇒ Q,
concat: concat(ll),
all: ∀x:A. B[x],
top: Top,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
prop: ℙ
Lemmas referenced :
list_induction,
list_wf,
top_wf,
equal_wf,
length_wf,
concat_wf,
reduce_wf,
nat_wf,
map_wf,
length_wf_nat,
reduce_nil_lemma,
map_nil_lemma,
length_of_nil_lemma,
map_cons_lemma,
reduce_cons_lemma,
subtype_base_sq,
int_subtype_base,
concat-cons,
length-append
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
lambdaEquality,
intEquality,
hypothesisEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
instantiate,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[ll:Top List List]. (||concat(ll)|| = l\_sum(map(\mlambda{}l.||l||;ll)))
Date html generated:
2016_05_14-PM-02_54_34
Last ObjectModification:
2015_12_26-PM-02_32_03
Theory : list_1
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