Nuprl Lemma : reg-seq-list-add_functionality_wrt_permutation
∀[L,L':ℝ List].
reg-seq-list-add(L) = reg-seq-list-add(L') ∈ {f:ℕ+ ⟶ ℤ| ||L||-regular-seq(f)} supposing permutation(ℝ;L;L')
Proof
Definitions occuring in Statement :
reg-seq-list-add: reg-seq-list-add(L),
real: ℝ,
regular-int-seq: k-regular-seq(f),
permutation: permutation(T;L1;L2),
length: ||as||,
list: T List,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
squash: ↓T,
cons: [a / b],
top: Top,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
true: True,
nat_plus: ℕ+,
guard: {T},
nat: ℕ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
sq_stable: SqStable(P),
real: ℝ
Lemmas referenced :
decidable__equal_int,
length_wf,
real_wf,
permutation_wf,
list_wf,
reg-seq-list-add_wf,
squash_wf,
true_wf,
permutation-length,
list-cases,
length_of_nil_lemma,
nil_wf,
product_subtype_list,
length_of_cons_lemma,
non_neg_length,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
sq_stable__regular-int-seq,
length_wf_nat,
nat_wf,
decidable__lt,
false_wf,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
equal_wf,
less_than_wf,
regular-int-seq_wf,
nat_plus_wf,
reg-seq-list-add-as-l_sum,
subtype_rel_list,
iff_weakening_equal,
l_sum_functionality_wrt_permutation,
map_wf,
permutation-map
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesis,
hypothesisEquality,
natural_numberEquality,
unionElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
imageElimination,
independent_isectElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
voidElimination,
voidEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
imageMemberEquality,
baseClosed,
dependent_set_memberEquality,
lambdaFormation,
setElimination,
rename,
independent_functionElimination,
addEquality,
minusEquality,
universeEquality,
functionEquality
Latex:
\mforall{}[L,L':\mBbbR{} List]. reg-seq-list-add(L) = reg-seq-list-add(L') supposing permutation(\mBbbR{};L;L')
Date html generated:
2017_10_02-PM-07_13_58
Last ObjectModification:
2017_07_28-AM-07_20_07
Theory : reals
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