Nuprl Lemma : no_repeats_nil
∀[T:Top]. no_repeats(T;[])
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
nil: [],
uall: ∀[x:A]. B[x],
top: Top
Definitions unfolded in proof :
no_repeats: no_repeats(T;l),
select: L[n],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
not: ¬A,
implies: P ⇒ Q,
false: False,
nat: ℕ,
guard: {T},
prop: ℙ
Lemmas referenced :
top_wf,
less_than_wf,
nat_wf,
equal_wf,
not_wf,
equal-wf-base,
less_than_irreflexivity,
less_than_transitivity1,
base_wf,
stuck-spread,
length_of_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
introduction,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
independent_functionElimination,
instantiate,
because_Cache,
lambdaEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Top]. no\_repeats(T;[])
Date html generated:
2016_05_14-AM-06_37_23
Last ObjectModification:
2016_01_06-PM-08_33_02
Theory : list_0
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