Nuprl Lemma : no_repeats_singleton_uiff
∀[T:Type]. ∀[x:T]. uiff(no_repeats(T;[x]);True)
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
cons: [a / b],
nil: [],
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
true: True,
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,
true: True,
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
no_repeats_wf,
cons_wf,
nil_wf,
no_repeats_singleton,
no_repeats_witness,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
natural_numberEquality,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
independent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. uiff(no\_repeats(T;[x]);True)
Date html generated:
2016_05_14-AM-06_46_07
Last ObjectModification:
2015_12_26-PM-00_26_07
Theory : list_0
Home
Index