Nuprl Lemma : expr-ln
∀x:ℝ. ((r0 < x) ⇒ (expr(ln(x)) = x))
Proof
Definitions occuring in Statement :
expr: expr(x),
ln: ln(a),
rless: x < y,
req: x = y,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
rless_wf,
int-to-real_wf,
real_wf,
expr_wf,
ln_wf,
req_wf,
rlog_wf,
rexp_wf,
rexp-rlog,
req_functionality,
req_transitivity,
expr-req,
rexp_functionality,
ln-req,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
dependent_set_memberEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
sqequalRule,
because_Cache,
independent_isectElimination,
productElimination
Latex:
\mforall{}x:\mBbbR{}. ((r0 < x) {}\mRightarrow{} (expr(ln(x)) = x))
Date html generated:
2017_10_04-PM-10_38_07
Last ObjectModification:
2017_06_24-AM-10_54_05
Theory : reals_2
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