Nuprl Lemma : remove-repeats-no_repeats-true
∀T:Type. ∀eq:EqDecider(T). ∀L:T List. (no_repeats(T;remove-repeats(eq;L)) ⇐⇒ True)
Proof
Definitions occuring in Statement :
remove-repeats: remove-repeats(eq;L),
no_repeats: no_repeats(T;l),
list: T List,
deq: EqDecider(T),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
true: True,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q
Lemmas referenced :
no_repeats_wf,
remove-repeats_wf,
remove-repeats-no_repeats,
true_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}eq:EqDecider(T). \mforall{}L:T List. (no\_repeats(T;remove-repeats(eq;L)) \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_14-PM-03_26_49
Last ObjectModification:
2015_12_26-PM-06_23_25
Theory : decidable!equality
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