Nuprl Lemma : permutation-reverse
∀[A:Type]. ∀L:A List. permutation(A;L;rev(L))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
reverse: rev(as),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
permutation: permutation(T;L1;L2),
cand: A c∧ B,
inject: Inj(A;B;f),
nat: ℕ,
le: A ≤ B,
true: True,
subtract: n - m,
subtype_rel: A ⊆r B,
ge: i ≥ j ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
subtract_wf,
length_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
itermAdd_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
decidable__lt,
lelt_wf,
int_seg_wf,
length-reverse,
permute_list_length,
list_wf,
inject_wf,
equal_wf,
reverse_wf,
permute_list_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
list_extensionality,
less_than_wf,
nat_wf,
select_wf,
squash_wf,
le_wf,
add-associates,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-commutes,
minus-add,
nat_properties,
true_wf,
select-reverse,
permute_list_select,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lambdaEquality,
dependent_set_memberEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
addEquality,
setElimination,
rename,
natural_numberEquality,
independent_pairFormation,
productElimination,
dependent_functionElimination,
unionElimination,
imageElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
because_Cache,
universeEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
functionExtensionality,
applyEquality,
applyLambdaEquality,
addLevel,
levelHypothesis,
minusEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}L:A List. permutation(A;L;rev(L))
Date html generated:
2017_04_17-AM-08_24_17
Last ObjectModification:
2017_02_27-PM-04_46_42
Theory : list_1
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