Nuprl Lemma : rlog-inv
∀y:{t:ℝ| r0 < t} . (rlog((r1/y)) = -(rlog(y)))
Proof
Definitions occuring in Statement :
rlog: rlog(x),
rdiv: (x/y),
rless: x < y,
req: x = y,
rminus: -(x),
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rsub: x - y,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
sq_stable: SqStable(P)
Lemmas referenced :
set_wf,
real_wf,
rless_wf,
int-to-real_wf,
rlog_wf,
rsub_wf,
rless-int,
radd_wf,
rminus_wf,
req_weakening,
req_functionality,
req_transitivity,
rlog-rdiv,
rsub_functionality,
rlog1,
radd-zero-both,
rdiv_wf,
sq_stable__rless,
rmul_preserves_rless,
rmul_wf,
rless_functionality,
rmul-zero-both,
rmul-rdiv-cancel2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
setElimination,
rename,
dependent_set_memberEquality,
because_Cache,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
imageMemberEquality,
baseClosed,
independent_isectElimination,
inrFormation,
imageElimination,
addLevel
Latex:
\mforall{}y:\{t:\mBbbR{}| r0 < t\} . (rlog((r1/y)) = -(rlog(y)))
Date html generated:
2016_10_26-PM-00_28_18
Last ObjectModification:
2016_09_19-AM-11_52_33
Theory : reals_2
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