Nuprl Lemma : inv-sinh_wf
∀[x:ℝ]. (inv-sinh(x) ∈ ℝ)
Proof
Definitions occuring in Statement :
inv-sinh: inv-sinh(x),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
inv-sinh: inv-sinh(x),
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
inv-sinh-domain,
ln_wf,
radd_wf,
rsqrt_wf,
rmul_wf,
int-to-real_wf,
rleq_wf,
real_wf,
req_wf,
rless_wf,
rlog_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
dependent_set_memberEquality,
isectElimination,
hypothesis,
natural_numberEquality,
productElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:\mBbbR{}]. (inv-sinh(x) \mmember{} \mBbbR{})
Date html generated:
2017_10_04-PM-10_43_04
Last ObjectModification:
2017_06_24-AM-10_44_21
Theory : reals_2
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