Nuprl Lemma : ln-expr
∀x:ℝ. (ln(expr(x)) = x)
Proof
Definitions occuring in Statement :
expr: expr(x),
ln: ln(a),
req: x = y,
real: ℝ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
expr_wf,
real_wf,
req_wf,
rexp_wf,
rless_wf,
int-to-real_wf,
rexp-positive,
rless_functionality,
req_weakening,
expr-req,
ln_wf,
rlog_wf,
rlog-rexp,
req_functionality,
req_transitivity,
ln-req,
rlog_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
dependent_set_memberEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
sqequalRule,
natural_numberEquality,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
productElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}x:\mBbbR{}. (ln(expr(x)) = x)
Date html generated:
2017_10_04-PM-10_38_11
Last ObjectModification:
2017_06_24-AM-11_00_11
Theory : reals_2
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