Nuprl Lemma : remove-repeats-no_repeats
∀T:Type. ∀eq:EqDecider(T). ∀L:T List. no_repeats(T;remove-repeats(eq;L))
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],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
top: Top,
deq: EqDecider(T),
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
cand: A c∧ B,
not: ¬A,
iff: P ⇐⇒ Q,
false: False
Lemmas referenced :
list_induction,
no_repeats_wf,
remove-repeats_wf,
list_wf,
remove_repeats_nil_lemma,
no_repeats_nil,
remove_repeats_cons_lemma,
no_repeats_cons,
filter_wf5,
bnot_wf,
l_member_wf,
no_repeats_filter,
member_filter_2,
assert_of_bnot,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
rename,
applyEquality,
setElimination,
setEquality,
productElimination,
independent_isectElimination,
because_Cache,
independent_pairFormation,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}eq:EqDecider(T). \mforall{}L:T List. no\_repeats(T;remove-repeats(eq;L))
Date html generated:
2016_05_14-PM-03_26_46
Last ObjectModification:
2015_12_26-PM-06_23_30
Theory : decidable!equality
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