Nuprl Lemma : sublist-rec-nil-iff
∀[T:Type]. ∀[l:T List]. uiff(sublist-rec(T;[];l);True)
Proof
Definitions occuring in Statement :
sublist-rec: sublist-rec(T;l1;l2),
nil: [],
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
true: True,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
true: True,
prop: ℙ
Lemmas referenced :
sublist-rec_wf,
nil_wf,
sublist-rec-nil,
true_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
introduction,
cut,
natural_numberEquality,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
rename,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. uiff(sublist-rec(T;[];l);True)
Date html generated:
2016_05_15-PM-03_33_55
Last ObjectModification:
2015_12_27-PM-01_12_53
Theory : general
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