Nuprl Lemma : rcos-seq-step
∀[n:ℕ]. (rcos-seq(n + 1) = (rcos-seq(n) + rcos(rcos-seq(n))))
Proof
Definitions occuring in Statement :
rcos-seq: rcos-seq(n),
rcos: rcos(x),
req: x = y,
radd: a + b,
nat: ℕ,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rcos-seq: rcos-seq(n),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
req_witness,
rcos-seq_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
radd_wf,
rcos_wf,
nat_wf,
primrec-unroll,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
add-subtract-cancel,
radd_rcos_wf,
set_wf,
real_wf,
req_wf,
sq_stable__req
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
because_Cache,
lambdaFormation,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
promote_hyp,
instantiate,
cumulativity,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[n:\mBbbN{}]. (rcos-seq(n + 1) = (rcos-seq(n) + rcos(rcos-seq(n))))
Date html generated:
2017_10_04-PM-10_22_33
Last ObjectModification:
2017_07_28-AM-08_48_33
Theory : reals_2
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