Nuprl Lemma : distinct_cons_lemma
∀as,a,s:Top. (distinct{s}([a / as]) ~ (∀br(:|s|) ∈ as. (¬b(r (=b) a))) ∧b distinct{s}(as))
Proof
Definitions occuring in Statement :
distinct: distinct{s}(ps),
ball: ball,
cons: [a / b],
band: p ∧b q,
bnot: ¬bb,
top: Top,
infix_ap: x f y,
all: ∀x:A. B[x],
sqequal: s ~ t,
set_eq: =b,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
distinct: distinct{s}(ps),
so_lambda: λ2x y.t[x; y],
member: t ∈ T,
top: Top,
so_apply: x[s1;s2],
band_mon: <𝔹,∧b>,
grp_op: *,
pi2: snd(t),
pi1: fst(t),
infix_ap: x f y
Lemmas referenced :
mon_htfor_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}as,a,s:Top. (distinct\{s\}([a / as]) \msim{} (\mforall{}\msubb{}r(:|s|) \mmember{} as. (\mneg{}\msubb{}(r (=\msubb{}) a))) \mwedge{}\msubb{} distinct\{s\}(as))
Date html generated:
2016_05_16-AM-07_37_26
Last ObjectModification:
2015_12_28-PM-05_45_18
Theory : list_2
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