Nuprl Lemma : rsin-positive-near-11/7
∀x:{x:ℝ| x ∈ ((r(41)/r(70)), (r(179)/r(70)))} . (r0 < rsin(x))
Proof
Definitions occuring in Statement :
rsin: rsin(x),
rooint: (l, u),
i-member: r ∈ I,
rdiv: (x/y),
rless: x < y,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
so_apply: x[s],
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
not: ¬A,
false: False,
top: Top,
cand: A c∧ B,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y,
rgt: x > y,
rsub: x - y,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
nat_plus: ℕ+,
int-to-real: r(n),
real: ℝ
Lemmas referenced :
set_wf,
real_wf,
i-member_wf,
rooint_wf,
rdiv_wf,
int-to-real_wf,
rless-int,
rless_wf,
rabs-difference-rsin-rleq,
rabs-difference-bound-rleq,
rleq_wf,
rsub_wf,
radd_wf,
less_than'_wf,
nat_plus_wf,
squash_wf,
sq_stable__and,
sq_stable__rleq,
member_rooint_lemma,
rmul_preserves_rleq,
rmul_wf,
rminus_wf,
rleq_weakening_equal,
rleq_functionality_wrt_implies,
rleq_weakening_rless,
uiff_transitivity,
rleq_functionality,
req_weakening,
rmul-rdiv-cancel2,
req_transitivity,
rmul-distrib,
radd_functionality,
rmul_over_rminus,
rminus_functionality,
rmul_comm,
radd_comm,
rmul-rdiv-cancel,
uiff_transitivity3,
true_wf,
rminus-int,
radd-int,
rabs_wf,
rsin_wf,
rless_functionality_wrt_implies,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
natural_numberEquality,
independent_isectElimination,
inrFormation,
dependent_functionElimination,
because_Cache,
productElimination,
independent_functionElimination,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
setElimination,
rename,
isect_memberEquality,
applyEquality,
minusEquality,
independent_pairEquality,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
imageElimination,
voidEquality,
addEquality,
dependent_set_memberFormation,
dependent_set_memberEquality,
computeAll
Latex:
\mforall{}x:\{x:\mBbbR{}| x \mmember{} ((r(41)/r(70)), (r(179)/r(70)))\} . (r0 < rsin(x))
Date html generated:
2016_10_26-PM-00_16_13
Last ObjectModification:
2016_09_12-PM-05_40_56
Theory : reals_2
Home
Index