Nuprl Lemma : l_sum_as_reduce
∀[L:ℤ List]. (reduce(λa,s. (s + a);0;L) ~ l_sum(L))
Proof
Definitions occuring in Statement :
l_sum: l_sum(L),
reduce: reduce(f;k;as),
list: T List,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
add: n + m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T)
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
l_sum_as_reduce_general,
add-zero,
l_sum_wf,
map_wf,
equal_wf,
squash_wf,
true_wf,
trivial_map,
l_member_wf,
iff_weakening_equal,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
hypothesisEquality,
natural_numberEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
lambdaFormation,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
dependent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[L:\mBbbZ{} List]. (reduce(\mlambda{}a,s. (s + a);0;L) \msim{} l\_sum(L))
Date html generated:
2017_04_17-AM-08_40_32
Last ObjectModification:
2017_02_27-PM-04_59_13
Theory : list_1
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