Nuprl Lemma : integral-zero
∀[a,b:ℝ]. (a_∫-b r0 dx = r0)
Proof
Definitions occuring in Statement :
integral: a_∫-b f[x] dx,
req: x = y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rfun: I ⟶ℝ,
prop: ℙ,
ifun: ifun(f;I),
all: ∀x:A. B[x],
top: Top,
real-fun: real-fun(f;a;b),
implies: P ⇒ Q,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
integral-const,
int-to-real_wf,
real_wf,
i-member_wf,
rccint_wf,
rmin_wf,
rmax_wf,
left_endpoint_rccint_lemma,
right_endpoint_rccint_lemma,
req_weakening,
req_wf,
set_wf,
ifun_wf,
rccint-icompact,
rmin-rleq-rmax,
integral_wf,
rmul_wf,
rsub_wf,
rmul-zero-both,
req_functionality
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
dependent_set_memberEquality,
sqequalRule,
lambdaEquality,
because_Cache,
setEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
independent_isectElimination,
setElimination,
rename,
productElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b:\mBbbR{}]. (a\_\mint{}\msupminus{}b r0 dx = r0)
Date html generated:
2018_05_22-PM-02_57_58
Last ObjectModification:
2017_10_23-PM-01_28_50
Theory : reals_2
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