Nuprl Lemma : rlog-rdiv
∀x,y:{t:ℝ| r0 < t} . (rlog((x/y)) = (rlog(x) - rlog(y)))
Proof
Definitions occuring in Statement :
rlog: rlog(x),
rdiv: (x/y),
rless: x < y,
rsub: x - y,
req: x = y,
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],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
itermConstant: "const",
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top,
uiff: uiff(P;Q),
rdiv: (x/y),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
set_wf,
real_wf,
rless_wf,
int-to-real_wf,
sq_stable__rless,
rmul_preserves_rless,
rdiv_wf,
rlog-rmul,
rmul_wf,
rinv_wf2,
req_weakening,
rless_functionality,
real_term_polynomial,
itermSubtract_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
real_term_value_const_lemma,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
req-iff-rsub-is-0,
req_transitivity,
rmul_functionality,
rmul-rinv,
req_functionality,
rlog_wf,
req_inversion,
rless_transitivity1,
rleq_weakening,
radd_wf,
rsub_wf,
rlog_functionality,
rsub_functionality,
itermAdd_wf,
real_term_value_add_lemma
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_functionElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
because_Cache,
independent_isectElimination,
inrFormation,
productElimination,
dependent_set_memberEquality,
addLevel,
computeAll,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}x,y:\{t:\mBbbR{}| r0 < t\} . (rlog((x/y)) = (rlog(x) - rlog(y)))
Date html generated:
2017_10_04-PM-10_26_27
Last ObjectModification:
2017_07_28-AM-08_50_00
Theory : reals_2
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