Nuprl Lemma : radd-list_functionality_wrt_permutation
∀[L1,L2:ℝ List].  radd-list(L1) = radd-list(L2) ∈ ℝ supposing permutation(ℝ;L1;L2)
Proof
Definitions occuring in Statement : 
radd-list: radd-list(L)
, 
real: ℝ
, 
permutation: permutation(T;L1;L2)
, 
list: T List
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
true: True
, 
decidable: Dec(P)
, 
nat_plus: ℕ+
, 
squash: ↓T
, 
top: Top
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
not: ¬A
, 
nequal: a ≠ b ∈ T 
, 
ge: i ≥ j 
, 
false: False
, 
assert: ↑b
, 
bnot: ¬bb
, 
guard: {T}
, 
sq_type: SQType(T)
, 
or: P ∨ Q
, 
prop: ℙ
, 
exists: ∃x:A. B[x]
, 
bfalse: ff
, 
ifthenelse: if b then t else f fi 
, 
and: P ∧ Q
, 
uiff: uiff(P;Q)
, 
btrue: tt
, 
it: ⋅
, 
unit: Unit
, 
bool: 𝔹
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
so_apply: x[s]
, 
so_lambda: λ2x.t[x]
, 
nat: ℕ
, 
has-valueall: has-valueall(a)
, 
has-value: (a)↓
, 
callbyvalueall: callbyvalueall, 
radd-list: radd-list(L)
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
reg-seq-list-add_functionality_wrt_permutation, 
less_than_wf, 
int_formula_prop_le_lemma, 
int_formula_prop_less_lemma, 
intformle_wf, 
intformless_wf, 
decidable__lt, 
decidable__equal_int, 
regular-int-seq_wf, 
nat_plus_wf, 
true_wf, 
squash_wf, 
accelerate_wf, 
permutation_wf, 
int-to-real_wf, 
int_formula_prop_wf, 
int_formula_prop_not_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_eq_lemma, 
int_formula_prop_and_lemma, 
intformnot_wf, 
itermConstant_wf, 
itermVar_wf, 
intformeq_wf, 
intformand_wf, 
full-omega-unsat, 
non_neg_length, 
neg_assert_of_eq_int, 
assert-bnot, 
bool_subtype_base, 
subtype_base_sq, 
bool_cases_sqequal, 
equal_wf, 
eqff_to_assert, 
assert_of_eq_int, 
eqtt_to_assert, 
bool_wf, 
length_wf, 
eq_int_wf, 
permutation-length, 
length_wf_nat, 
int-value-type, 
le_wf, 
set-value-type, 
nat_wf, 
value-type-has-value, 
valueall-type-real-list, 
evalall-reduce, 
real-valueall-type, 
list-valueall-type, 
real_wf, 
list_wf, 
valueall-type-has-valueall
Rules used in proof : 
baseClosed, 
imageMemberEquality, 
dependent_set_memberEquality, 
rename, 
setElimination, 
functionEquality, 
setEquality, 
imageElimination, 
applyEquality, 
axiomEquality, 
independent_pairFormation, 
voidEquality, 
isect_memberEquality, 
int_eqEquality, 
approximateComputation, 
voidElimination, 
independent_functionElimination, 
cumulativity, 
instantiate, 
dependent_functionElimination, 
promote_hyp, 
dependent_pairFormation, 
productElimination, 
equalitySymmetry, 
equalityTransitivity, 
equalityElimination, 
unionElimination, 
lambdaFormation, 
natural_numberEquality, 
lambdaEquality, 
intEquality, 
because_Cache, 
callbyvalueReduce, 
hypothesisEquality, 
independent_isectElimination, 
hypothesis, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
sqequalRule, 
cut, 
introduction, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[L1,L2:\mBbbR{}  List].    radd-list(L1)  =  radd-list(L2)  supposing  permutation(\mBbbR{};L1;L2)
Date html generated:
2018_05_22-PM-01_20_36
Last ObjectModification:
2018_05_21-AM-00_02_22
Theory : reals
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