Nuprl Lemma : distinct_nil_lemma
∀s:Top. (distinct{s}([]) ~ tt)
Proof
Definitions occuring in Statement :
distinct: distinct{s}(ps),
nil: [],
btrue: tt,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
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_id: e,
pi2: snd(t),
pi1: fst(t)
Lemmas referenced :
mon_htfor_nil_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{}s:Top. (distinct\{s\}([]) \msim{} tt)
Date html generated:
2016_05_16-AM-07_37_25
Last ObjectModification:
2015_12_28-PM-05_45_17
Theory : list_2
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