Nuprl Lemma : list-to-set-is-remove-repeats
∀[T:Type]. ∀eq:EqDecider(T). ∀L:T List. permutation(T;list-to-set(eq;L);remove-repeats(eq;L))
Proof
Definitions occuring in Statement :
remove-repeats: remove-repeats(eq;L),
list-to-set: list-to-set(eq;L),
permutation: permutation(T;L1;L2),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
deq: EqDecider(T),
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
eqof: eqof(d),
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False,
ge: i ≥ j ,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
permutation-iff-count1,
safe-assert-deq,
assert_wf,
equal_wf,
assert_witness,
list-to-set_wf,
remove-repeats_wf,
list-to-set-property,
no-repeats-iff-count,
remove-repeats-no_repeats,
list_wf,
deq_wf,
decidable__le,
length_wf,
filter_wf5,
subtype_rel_dep_function,
l_member_wf,
bool_wf,
set_wf,
subtype_rel_self,
remove-repeats_property,
l_member-iff-length-filter,
equal-wf-T-base,
non_neg_length,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
setElimination,
rename,
hypothesis,
independent_functionElimination,
independent_pairFormation,
sqequalRule,
because_Cache,
productElimination,
independent_isectElimination,
applyEquality,
cumulativity,
independent_pairEquality,
lambdaEquality,
axiomEquality,
universeEquality,
natural_numberEquality,
setEquality,
unionElimination,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
voidElimination,
instantiate,
baseClosed,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}L:T List. permutation(T;list-to-set(eq;L);remove-repeats(eq;L))
Date html generated:
2017_04_17-AM-09_11_30
Last ObjectModification:
2017_02_27-PM-05_19_29
Theory : decidable!equality
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