Nuprl Lemma : arcsine_deriv_functionality
∀[x:{x:ℝ| x ∈ (r(-1), r1)} ]. ∀[y:ℝ]. arcsine_deriv(x) = arcsine_deriv(y) supposing x = y
Proof
Definitions occuring in Statement :
arcsine_deriv: arcsine_deriv(x),
rooint: (l, u),
i-member: r ∈ I,
req: x = y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
minus: -n,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
cand: A c∧ B,
guard: {T},
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
arcsine_deriv: arcsine_deriv(x),
subtype_rel: A ⊆r B,
rneq: x ≠ y,
or: P ∨ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
arcsine-root-bounds,
member_rooint_lemma,
sq_stable__req,
arcsine_deriv_wf,
rless_wf,
int-to-real_wf,
rless_transitivity1,
rleq_weakening,
req_inversion,
rless_transitivity2,
req_witness,
i-member_wf,
rooint_wf,
req_wf,
real_wf,
set_wf,
rdiv_wf,
rsqrt_wf,
rleq_weakening_rless,
rsub_wf,
rmul_wf,
rleq_wf,
rsqrt-positive,
req_weakening,
req_functionality,
rdiv_functionality,
rsqrt_functionality,
rsub_functionality,
rmul_functionality
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
setElimination,
thin,
rename,
sqequalHypSubstitution,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalRule,
isectElimination,
productElimination,
dependent_set_memberEquality,
hypothesisEquality,
independent_pairFormation,
productEquality,
minusEquality,
natural_numberEquality,
independent_functionElimination,
independent_isectElimination,
because_Cache,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
applyEquality,
inrFormation
Latex:
\mforall{}[x:\{x:\mBbbR{}| x \mmember{} (r(-1), r1)\} ]. \mforall{}[y:\mBbbR{}]. arcsine\_deriv(x) = arcsine\_deriv(y) supposing x = y
Date html generated:
2016_10_26-PM-00_41_11
Last ObjectModification:
2016_09_12-PM-05_45_27
Theory : reals_2
Home
Index