Nuprl Lemma : index-split-permutation
∀[T:Type]. ∀L:T List. ∀ids:ℕ List. let L1,L2 = index-split(L;ids) in permutation(T;L;L1 @ L2)
Proof
Definitions occuring in Statement :
index-split: index-split(L;idxs),
permutation: permutation(T;L1;L2),
append: as @ bs,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
spread: spread def,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
index-split: index-split(L;idxs),
let: let,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
less_than: a < b
Lemmas referenced :
permute-to-front-permutation,
int_seg_wf,
length_wf,
equal_wf,
list_wf,
nat_wf,
length-filter,
int-list-member_wf,
subtype_rel_list,
upto_wf,
length_upto,
length_wf_nat,
non_neg_length,
filter_wf5,
l_member_wf,
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,
decidable__lt,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
lelt_wf,
append_firstn_lastn_sq,
permute-to-front_wf,
top_wf,
permutation-length,
intformeq_wf,
int_formula_prop_eq_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
natural_numberEquality,
addEquality,
cumulativity,
hypothesis,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
universeEquality,
intEquality,
lambdaEquality,
applyEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
dependent_set_memberEquality,
independent_pairFormation,
setEquality,
unionElimination,
productElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}ids:\mBbbN{} List. let L1,L2 = index-split(L;ids) in permutation(T;L;L1 @ L2)
Date html generated:
2018_05_21-PM-07_32_42
Last ObjectModification:
2017_07_26-PM-05_07_47
Theory : general
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