Nuprl Lemma : rsin-strictly-increasing
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,
rooint: (l, u),
rminus: -(x)
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
rfun: I ⟶ℝ,
prop: ℙ,
so_apply: x[s],
subinterval: I ⊆ J ,
top: Top,
true: True,
and: P ∧ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
derivative-implies-strictly-increasing,
rooint_wf,
rminus_wf,
halfpi_wf,
halfpi-interval-proper,
rsin_wf,
real_wf,
i-member_wf,
rcos_wf,
rcos-positive,
set_wf,
derivative_functionality_wrt_subinterval,
riiint_wf,
member_rooint_lemma,
member_riiint_lemma,
rless_wf,
deriviative-rsin,
function-is-continuous,
req_functionality,
rcos_functionality,
req_weakening,
req_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
isectElimination,
hypothesis,
independent_functionElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
setEquality,
because_Cache,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
productEquality,
independent_isectElimination,
productElimination
Latex:
rsin(x) strictly-increasing for x \mmember{} (-(\mpi{}/2), \mpi{}/2)
Date html generated:
2016_10_26-PM-00_26_03
Last ObjectModification:
2016_09_12-PM-05_43_53
Theory : reals_2
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