Nuprl Lemma : radd-list-cons
∀[L:ℝ List]. ∀[x:ℝ]. (radd-list([x / L]) = (x + radd-list(L)))
Proof
Definitions occuring in Statement :
req: x = y,
radd: a + b,
radd-list: radd-list(L),
real: ℝ,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
radd: a + b,
implies: P ⇒ Q,
real: ℝ,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ,
all: ∀x:A. B[x],
top: Top,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
radd-list: radd-list(L),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
ge: i ≥ j ,
nequal: a ≠ b ∈ T ,
le: A ≤ B,
decidable: Dec(P),
int-to-real: r(n),
cons: [a / b]
Lemmas referenced :
req-iff-bdd-diff,
radd-list_wf-bag,
cons_wf,
real_wf,
list-subtype-bag,
subtype_rel_self,
radd_wf,
req_witness,
list_wf,
accelerate_wf,
less_than_wf,
reg-seq-list-add_wf,
nil_wf,
length_of_cons_lemma,
length_of_nil_lemma,
nat_plus_wf,
regular-int-seq_wf,
length_wf,
bdd-diff_wf,
squash_wf,
true_wf,
reg-seq-list-add-as-l_sum,
iff_weakening_equal,
map_cons_lemma,
map_nil_lemma,
l_sum_cons_lemma,
l_sum_nil_lemma,
bdd-diff_functionality,
bdd-diff_weakening,
accelerate-bdd-diff,
valueall-type-has-valueall,
list-valueall-type,
real-valueall-type,
evalall-reduce,
valueall-type-real-list,
value-type-has-value,
int-value-type,
nat_wf,
set-value-type,
le_wf,
length_wf_nat,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
non_neg_length,
intformle_wf,
int_formula_prop_le_lemma,
add_nat_plus,
nat_plus_properties,
decidable__lt,
add-is-int-iff,
intformnot_wf,
intformless_wf,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
false_wf,
int-to-real_wf,
list-cases,
decidable__equal_int,
itermMultiply_wf,
int_term_value_mul_lemma,
product_subtype_list,
bdd-diff-add,
add-commutes,
add-associates,
subtype_rel_list,
l_sum_wf,
map_wf,
add_functionality_wrt_eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
sqequalRule,
productElimination,
independent_functionElimination,
isect_memberEquality,
lambdaEquality,
setElimination,
rename,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
voidElimination,
voidEquality,
setEquality,
functionEquality,
intEquality,
functionExtensionality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
callbyvalueReduce,
addEquality,
lambdaFormation,
unionElimination,
equalityElimination,
dependent_pairFormation,
int_eqEquality,
computeAll,
promote_hyp,
instantiate,
cumulativity,
applyLambdaEquality,
pointwiseFunctionality,
baseApply,
closedConclusion,
hypothesis_subsumption
Latex:
\mforall{}[L:\mBbbR{} List]. \mforall{}[x:\mBbbR{}]. (radd-list([x / L]) = (x + radd-list(L)))
Date html generated:
2017_10_02-PM-07_15_23
Last ObjectModification:
2017_07_28-AM-07_20_26
Theory : reals
Home
Index