Nuprl Lemma : no_repeats-insert
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[a:T]. ∀[L:T List]. no_repeats(T;insert(a;L)) supposing no_repeats(T;L)
Proof
Definitions occuring in Statement :
insert: insert(a;L),
no_repeats: no_repeats(T;l),
list: T List,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
insert_property,
no_repeats_witness,
insert_wf,
no_repeats_wf,
list_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
dependent_functionElimination,
productElimination,
sqequalRule,
isect_memberEquality,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[a:T]. \mforall{}[L:T List].
no\_repeats(T;insert(a;L)) supposing no\_repeats(T;L)
Date html generated:
2016_05_14-AM-06_54_09
Last ObjectModification:
2015_12_26-PM-00_19_50
Theory : list_0
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