Nuprl Lemma : permute_list_select
∀[T:Type]. ∀[L:T List]. ∀[f:ℕ||L|| ⟶ ℕ||L||]. ∀[i:ℕ||L||]. ((L o f)[i] = L[f i] ∈ T)
Proof
Definitions occuring in Statement :
permute_list: (L o f),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
permute_list: (L o f),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
ge: i ≥ j ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
le: A ≤ B,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
not: ¬A,
implies: P ⇒ Q,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
mklist_select,
length_wf_nat,
int_seg_wf,
length_wf,
select_wf,
non_neg_length,
int_seg_properties,
decidable__le,
lelt_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
cumulativity,
hypothesis,
natural_numberEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
functionEquality,
lambdaEquality,
applyEquality,
functionExtensionality,
independent_isectElimination,
setElimination,
rename,
productElimination,
dependent_functionElimination,
dependent_set_memberEquality,
independent_pairFormation,
unionElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
independent_functionElimination,
voidElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidEquality,
computeAll,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[f:\mBbbN{}||L|| {}\mrightarrow{} \mBbbN{}||L||]. \mforall{}[i:\mBbbN{}||L||]. ((L o f)[i] = L[f i])
Date html generated:
2017_04_17-AM-08_09_34
Last ObjectModification:
2017_02_27-PM-04_37_52
Theory : list_1
Home
Index