Nuprl Lemma : length-remove-repeats-le
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List]. (||remove-repeats(eq;L)|| ≤ ||L||)
Proof
Definitions occuring in Statement :
remove-repeats: remove-repeats(eq;L),
length: ||as||,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
le: A ≤ B,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
squash: ↓T,
deq: EqDecider(T),
uimplies: b supposing a,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Lemmas referenced :
less_than'_wf,
deq_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
itermVar_wf,
itermSubtract_wf,
itermAdd_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
non_neg_length,
iff_weakening_equal,
length-filter-bnot,
subtract_wf,
l_member_wf,
bnot_wf,
filter_wf5,
add_functionality_wrt_eq,
true_wf,
squash_wf,
length_of_cons_lemma,
remove_repeats_cons_lemma,
false_wf,
length_of_nil_lemma,
remove_repeats_nil_lemma,
list_wf,
remove-repeats_wf,
length_wf,
le_wf,
list_induction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
rename,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
setElimination,
setEquality,
because_Cache,
independent_isectElimination,
addEquality,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
computeAll,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:T List]. (||remove-repeats(eq;L)|| \mleq{} ||L||)
Date html generated:
2016_05_14-PM-03_26_41
Last ObjectModification:
2016_01_14-PM-11_22_12
Theory : decidable!equality
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