Nuprl Lemma : ln-req
∀[a:{a:ℝ| r0 < a} ]. (ln(a) = rlog(a))
Proof
Definitions occuring in Statement :
ln: ln(a),
rlog: rlog(x),
rless: x < y,
req: x = y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
ln_wf,
rless_wf,
int-to-real_wf,
set_wf,
real_wf,
req_wf,
rlog_wf,
sq_stable__req,
equal_wf,
req_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
dependent_set_memberEquality,
hypothesisEquality,
hypothesis,
isectElimination,
natural_numberEquality,
sqequalRule,
lambdaEquality,
because_Cache,
lambdaFormation,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
applyEquality,
setEquality
Latex:
\mforall{}[a:\{a:\mBbbR{}| r0 < a\} ]. (ln(a) = rlog(a))
Date html generated:
2017_10_04-PM-10_35_33
Last ObjectModification:
2017_06_06-AM-10_55_16
Theory : reals_2
Home
Index