Nuprl Lemma : rng_prod_empty_lemma
∀f,r:Top. (Π(r) 0 ≤ i < 0. f[i] ~ 1)
Proof
Definitions occuring in Statement :
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
natural_number: $n,
sqequal: s ~ t,
rng_prod: rng_prod,
rng_one: 1
Definitions unfolded in proof :
member: t ∈ T,
bfalse: ff,
ifthenelse: if b then t else f fi ,
subtract: n - m,
lt_int: i <z j,
ycomb: Y,
itop: Π(op,id) lb ≤ i < ub. E[i],
grp_id: e,
pi1: fst(t),
pi2: snd(t),
grp_op: *,
mul_mon_of_rng: r↓xmn,
mon_itop: Π lb ≤ i < ub. E[i],
rng_prod: rng_prod,
all: ∀x:A. B[x]
Lemmas referenced :
top_wf
Rules used in proof :
extract_by_obid,
introduction,
hypothesis,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}f,r:Top. (\mPi{}(r) 0 \mleq{} i < 0. f[i] \msim{} 1)
Date html generated:
2018_05_21-PM-09_33_26
Last ObjectModification:
2017_12_11-PM-06_53_08
Theory : matrices
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