Nuprl Lemma : no_repeats_nil_uiff
∀[T:Top]. uiff(no_repeats(T;[]);True)
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
nil: [],
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
true: True
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],
uiff: uiff(P;Q),
and: P ∧ Q,
true: True,
prop: ℙ,
so_lambda: λ2x.t[x],
nat: ℕ,
false: False,
guard: {T},
implies: P ⇒ Q,
so_apply: x[s],
not: ¬A
Lemmas referenced :
top_wf,
true_wf,
less_than_irreflexivity,
less_than_transitivity1,
equal-wf-base,
equal_wf,
not_wf,
less_than_wf,
isect_wf,
nat_wf,
uall_wf,
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,
independent_pairFormation,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
because_Cache,
setElimination,
rename,
hypothesisEquality,
independent_functionElimination,
instantiate,
dependent_functionElimination,
productElimination,
independent_pairEquality
Latex:
\mforall{}[T:Top]. uiff(no\_repeats(T;[]);True)
Date html generated:
2016_05_14-AM-06_37_27
Last ObjectModification:
2016_01_06-PM-08_33_17
Theory : list_0
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