Nuprl Lemma : no_repeats_singleton
∀[T:Type]. ∀[x:T]. no_repeats(T;[x])
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
cand: A c∧ B,
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
no_repeats_cons,
nil_wf,
no_repeats_nil,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
l_member_wf,
no_repeats_witness,
cons_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
lambdaFormation,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. no\_repeats(T;[x])
Date html generated:
2016_05_14-AM-06_46_02
Last ObjectModification:
2015_12_26-PM-00_25_55
Theory : list_0
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