Nuprl Lemma : radd-list_wf
∀[L:ℝ List]. (radd-list(L) ∈ ℝ)
Proof
Definitions occuring in Statement :
radd-list: radd-list(L),
real: ℝ,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
radd-list: radd-list(L),
callbyvalueall: callbyvalueall,
uimplies: b supposing a,
has-value: (a)↓,
has-valueall: has-valueall(a),
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nat_plus: ℕ+,
ge: i ≥ j ,
nequal: a ≠ b ∈ T ,
decidable: Dec(P),
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top
Lemmas referenced :
real-list-has-valueall,
evalall-reduce,
list_wf,
real_wf,
valueall-type-real-list,
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
length_wf_nat,
eq_int_wf,
length_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
int-to-real_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
accelerate_wf,
non_neg_length,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
less_than_wf,
reg-seq-list-add_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
callbyvalueReduce,
independent_isectElimination,
intEquality,
lambdaEquality,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
dependent_set_memberEquality,
int_eqEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll,
axiomEquality
Latex:
\mforall{}[L:\mBbbR{} List]. (radd-list(L) \mmember{} \mBbbR{})
Date html generated:
2017_10_02-PM-07_14_07
Last ObjectModification:
2017_07_28-AM-07_20_11
Theory : reals
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