Nuprl Lemma : lsum_nil_lemma
∀f:Top. (Σ(f[x] | x ∈ []) ~ 0)
Proof
Definitions occuring in Statement :
lsum: Σ(f[x] | x ∈ L),
nil: [],
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
lsum: Σ(f[x] | x ∈ L),
member: t ∈ T,
top: Top
Lemmas referenced :
istype-top,
map_nil_lemma,
istype-void,
l_sum_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}f:Top. (\mSigma{}(f[x] | x \mmember{} []) \msim{} 0)
Date html generated:
2020_05_19-PM-09_46_45
Last ObjectModification:
2019_11_12-PM-11_19_24
Theory : list_1
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