Nuprl Lemma : permutation-rotate
∀[A:Type]. ∀as,bs:A List. permutation(A;as @ bs;bs @ as)
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
permutation: permutation(T;L1;L2),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
exists: ∃x:A. B[x],
int_seg: {i..j-},
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
lelt: i ≤ j < k,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
prop: ℙ,
less_than: a < b,
squash: ↓T,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
less_than': less_than'(a;b),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
permute_list: (L o f),
inject: Inj(A;B;f),
nat: ℕ
Lemmas referenced :
list_wf,
lt_int_wf,
length_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
add-member-int_seg2,
non_neg_length,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermSubtract_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
subtract_wf,
add-is-int-iff,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
false_wf,
lelt_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
int_seg_properties,
int_seg_wf,
inject_wf,
append_wf,
permute_list_wf,
subtype_rel_dep_function,
int_seg_subtype,
le_wf,
length_append,
subtype_rel_list,
top_wf,
iff_weakening_equal,
length-append,
equal-wf-T-base,
assert_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
le_int_wf,
bnot_wf,
uiff_transitivity,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
list_extensionality,
mklist_wf,
length_wf_nat,
select_wf,
add_nat_wf,
int_seg_subtype_nat,
nat_wf,
nat_properties,
mklist_length,
all_wf,
squash_wf,
true_wf,
mklist_select,
select_append_front,
select_append_back,
add-subtract-cancel
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
universeEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
dependent_pairFormation,
lambdaEquality,
setElimination,
rename,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
natural_numberEquality,
addEquality,
dependent_set_memberEquality,
independent_pairFormation,
dependent_functionElimination,
int_eqEquality,
intEquality,
computeAll,
imageElimination,
pointwiseFunctionality,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
instantiate,
independent_functionElimination,
productEquality,
functionExtensionality,
applyEquality,
imageMemberEquality,
applyLambdaEquality,
functionEquality
Latex:
\mforall{}[A:Type]. \mforall{}as,bs:A List. permutation(A;as @ bs;bs @ as)
Date html generated:
2017_04_17-AM-08_10_46
Last ObjectModification:
2017_02_27-PM-04_38_43
Theory : list_1
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