Nuprl Lemma : no_repeats_functionality_wrt_permutation
∀[A:Type]. ∀as1,as2:A List. (permutation(A;as1;as2) ⇒ (no_repeats(A;as1) ⇐⇒ no_repeats(A;as2)))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
no_repeats: no_repeats(T;l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
no_repeats: no_repeats(T;l),
uimplies: b supposing a,
not: ¬A,
false: False,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
less_than': less_than'(a;b),
inject: Inj(A;B;f)
Lemmas referenced :
no_repeats_witness,
no_repeats_wf,
permutation_wf,
list_wf,
length_wf_nat,
equal_wf,
nat_wf,
select_wf,
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,
less_than_wf,
length_wf,
permute_list_wf,
int_seg_wf,
permute_list_length,
lelt_wf,
squash_wf,
true_wf,
permute_list_select,
iff_weakening_equal,
non_neg_length,
decidable__lt,
int_seg_properties,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_subtype_nat,
false_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
permutation_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairEquality,
extract_by_obid,
isectElimination,
independent_functionElimination,
hypothesis,
cumulativity,
universeEquality,
lambdaFormation,
dependent_set_memberEquality,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
voidElimination,
because_Cache,
equalityTransitivity,
independent_isectElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll,
functionExtensionality,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[A:Type]. \mforall{}as1,as2:A List. (permutation(A;as1;as2) {}\mRightarrow{} (no\_repeats(A;as1) \mLeftarrow{}{}\mRightarrow{} no\_repeats(A;as2)))
Date html generated:
2017_04_17-AM-08_12_17
Last ObjectModification:
2017_02_27-PM-04_39_38
Theory : list_1
Home
Index