Nuprl Lemma : remove-repeats-length-leq
∀[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],
prop: ℙ,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
top: Top,
less_than': less_than'(a;b),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
sq_type: SQType(T),
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Lemmas referenced :
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
length_of_cons_lemma,
int_subtype_base,
subtype_base_sq,
remove-repeats-append-one-member,
iff_weakening_equal,
append_wf,
nil_wf,
cons_wf,
remove-repeats-append,
true_wf,
squash_wf,
list_ind_nil_lemma,
list_ind_cons_lemma,
false_wf,
length_of_nil_lemma,
remove_repeats_nil_lemma,
deq_wf,
less_than'_wf,
list_wf,
remove-repeats_wf,
length_wf,
le_wf,
list_induction
Rules used in proof :
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
lambdaFormation,
rename,
because_Cache,
dependent_functionElimination,
universeEquality,
isect_memberFormation,
introduction,
productElimination,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
natural_numberEquality,
applyEquality,
imageElimination,
intEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
unionElimination,
instantiate,
cumulativity,
addEquality,
dependent_pairFormation,
int_eqEquality,
computeAll
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_29_16
Last ObjectModification:
2016_01_14-PM-11_21_21
Theory : decidable!equality
Home
Index