Nuprl Lemma : unshuffle-map'
∀[f:ℕ ⟶ Top]. ∀[m:ℕ]. ∀[r:ℕ2]. (unshuffle(map(f;upto((2 * m) + r))) ~ map(λi.<f (2 * i), f ((2 * i) + 1)>;upto(m)))
Proof
Definitions occuring in Statement :
unshuffle: unshuffle(L),
upto: upto(n),
map: map(f;as),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
pair: <a, b>,
multiply: n * m,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
nat_plus: ℕ+,
squash: ↓T,
subtract: n - m,
subtype_rel: A ⊆r B,
true: True,
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
length_upto,
le_wf,
false_wf,
int_seg_subtype_nat,
subtype_rel_list,
unshuffle-odd-length,
nil_wf,
true_wf,
squash_wf,
cons_wf,
zero-add,
add-commutes,
add-swap,
add-associates,
upto_wf,
append_wf,
list_subtype_base,
list_wf,
less_than_wf,
int_term_value_mul_lemma,
int_term_value_add_lemma,
itermMultiply_wf,
itermAdd_wf,
upto_decomp1,
lelt_wf,
decidable__lt,
decidable__le,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
int_seg_properties,
set_subtype_base,
add-zero,
top_wf,
nat_wf,
int_seg_wf,
int_subtype_base,
subtype_base_sq,
decidable__equal_int,
unshuffle-map
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
setElimination,
rename,
natural_numberEquality,
unionElimination,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
sqequalAxiom,
isect_memberEquality,
functionEquality,
multiplyEquality,
productElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
addEquality,
applyEquality,
imageElimination,
minusEquality,
imageMemberEquality,
baseClosed,
lambdaFormation
Latex:
\mforall{}[f:\mBbbN{} {}\mrightarrow{} Top]. \mforall{}[m:\mBbbN{}]. \mforall{}[r:\mBbbN{}2].
(unshuffle(map(f;upto((2 * m) + r))) \msim{} map(\mlambda{}i.<f (2 * i), f ((2 * i) + 1)>upto(m)))
Date html generated:
2016_05_14-PM-03_17_40
Last ObjectModification:
2016_01_15-AM-07_11_02
Theory : list_1
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