Nuprl Lemma : no_repeats-permute
∀[T:Type]. ∀[as,bs:T List]. uiff(no_repeats(T;as @ bs);no_repeats(T;bs @ as))
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
append: as @ bs,
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
no_repeats: no_repeats(T;l),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
false: False,
prop: ℙ,
nat: ℕ,
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
true: True,
guard: {T},
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m
Lemmas referenced :
equal_wf,
select_wf,
append_wf,
length-append,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
not_wf,
nat_wf,
less_than_wf,
length_wf,
uall_wf,
isect_wf,
list_wf,
decidable__lt,
lelt_wf,
add_nat_wf,
length_wf_nat,
add-is-int-iff,
itermAdd_wf,
intformeq_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
false_wf,
le_wf,
intformless_wf,
int_formula_prop_less_lemma,
decidable__equal_int,
equal-wf-base,
int_subtype_base,
squash_wf,
true_wf,
select_append_front,
iff_weakening_equal,
select_append_back,
add-associates,
minus-one-mul,
add-swap,
add-mul-special,
zero-mul,
add-zero,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
non_neg_length,
no_repeats_witness,
no_repeats_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
isect_memberFormation,
introduction,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
setElimination,
rename,
independent_isectElimination,
isect_memberEquality,
voidEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_set_memberEquality,
productElimination,
addEquality,
applyLambdaEquality,
pointwiseFunctionality,
promote_hyp,
imageElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
imageMemberEquality,
independent_pairEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. uiff(no\_repeats(T;as @ bs);no\_repeats(T;bs @ as))
Date html generated:
2018_05_21-PM-07_39_48
Last ObjectModification:
2017_07_26-PM-05_14_00
Theory : general
Home
Index