Nuprl Lemma : rcos-seq_wf
∀[n:ℕ]. (rcos-seq(n) ∈ ℝ)
Proof
Definitions occuring in Statement :
rcos-seq: rcos-seq(n),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rcos-seq: rcos-seq(n),
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
primrec_wf,
real_wf,
int-rdiv_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
nequal_wf,
int-to-real_wf,
radd_rcos_wf,
req_wf,
radd_wf,
rcos_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
addLevel,
lambdaFormation,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
baseClosed,
lambdaEquality,
applyEquality,
setElimination,
rename,
setEquality,
because_Cache,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (rcos-seq(n) \mmember{} \mBbbR{})
Date html generated:
2016_10_26-PM-00_17_16
Last ObjectModification:
2016_09_12-PM-05_41_28
Theory : reals_2
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