Nuprl Lemma : IVTlog_wf
∀a:{a:ℝ| r0 < a} . (IVTlog(a) ∈ {x:ℝ| x = rlog(a)} )
Proof
Definitions occuring in Statement :
IVTlog: IVTlog(a),
rlog: rlog(x),
rless: x < y,
req: x = y,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
IVTlog: IVTlog(a),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
exists: ∃x:A. B[x],
implies: P ⇒ Q,
pi1: fst(t)
Lemmas referenced :
log-by-IVT,
subtype_rel_self,
real_wf,
rless_wf,
int-to-real_wf,
req_wf,
rlog_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
setElimination,
thin,
rename,
sqequalRule,
applyEquality,
instantiate,
extract_by_obid,
hypothesis,
introduction,
sqequalHypSubstitution,
isectElimination,
functionEquality,
setEquality,
natural_numberEquality,
hypothesisEquality,
productEquality,
dependent_set_memberEquality_alt,
universeIsType,
inhabitedIsType,
productElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
setIsType
Latex:
\mforall{}a:\{a:\mBbbR{}| r0 < a\} . (IVTlog(a) \mmember{} \{x:\mBbbR{}| x = rlog(a)\} )
Date html generated:
2019_10_31-AM-06_10_29
Last ObjectModification:
2019_01_28-PM-01_46_43
Theory : reals_2
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