Nuprl Lemma : rcos-bounds
∀x:ℝ. (rcos(x) ∈ [r(-1), r1])
Proof
Definitions occuring in Statement :
rcos: rcos(x),
rccint: [l, u],
i-member: r ∈ I,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
minus: -n,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
rabs-rcos-rleq,
member_rccint_lemma,
istype-void,
rabs-rleq-iff,
rcos_wf,
int-to-real_wf,
rleq_wf,
squash_wf,
true_wf,
rminus-int,
subtype_rel_self,
iff_weakening_equal,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberEquality_alt,
voidElimination,
hypothesis,
isectElimination,
natural_numberEquality,
productElimination,
independent_functionElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeIsType,
inhabitedIsType,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
independent_pairFormation
Latex:
\mforall{}x:\mBbbR{}. (rcos(x) \mmember{} [r(-1), r1])
Date html generated:
2019_10_30-AM-11_41_44
Last ObjectModification:
2019_05_23-AM-10_12_42
Theory : reals_2
Home
Index