Nuprl Lemma : rsin-strictly-increasing2
rsin(x) strictly-increasing for x ∈ [-(π/2), π/2]
Proof
Definitions occuring in Statement :
halfpi: π/2,
rsin: rsin(x),
strictly-increasing-on-interval: f[x] strictly-increasing for x ∈ I,
rccint: [l, u],
rminus: -(x)
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
rfun: I ⟶ℝ,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
top: Top,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
rsin-strictly-increasing,
strictly-increasing-on-closed-interval2,
rminus_wf,
halfpi_wf,
rsin_wf,
real_wf,
i-member_wf,
rccint_wf,
req_functionality,
rsin_functionality,
req_weakening,
req_wf,
int-to-real_wf,
rsin-bounds,
member_rccint_lemma,
istype-void,
rleq_wf,
squash_wf,
true_wf,
rminus-int,
subtype_rel_self,
iff_weakening_equal,
rleq_functionality,
req_transitivity,
rsin-rminus,
rminus_functionality,
rsin-halfpi
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
isectElimination,
hypothesis,
sqequalRule,
lambdaEquality_alt,
setElimination,
rename,
hypothesisEquality,
setIsType,
universeIsType,
independent_functionElimination,
lambdaFormation_alt,
because_Cache,
independent_isectElimination,
productElimination,
independent_pairFormation,
natural_numberEquality,
isect_memberEquality_alt,
voidElimination,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality
Latex:
rsin(x) strictly-increasing for x \mmember{} [-(\mpi{}/2), \mpi{}/2]
Date html generated:
2019_10_30-AM-11_43_56
Last ObjectModification:
2019_05_23-AM-10_13_41
Theory : reals_2
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