Nuprl Lemma : sinh_wf
∀[x:ℝ]. (sinh(x) ∈ ℝ)
Proof
Definitions occuring in Statement :
sinh: sinh(x),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
guard: {T},
all: ∀x:A. B[x],
sq_type: SQType(T),
uimplies: b supposing a,
implies: P ⇒ Q,
not: ¬A,
nequal: a ≠ b ∈ T ,
true: True,
int_nzero: ℤ-o,
sinh: sinh(x),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rminus_wf,
rexp_wf,
req_wf,
real_wf,
expr_wf,
rsub_wf,
nequal_wf,
true_wf,
equal-wf-base,
int_subtype_base,
subtype_base_sq,
int-rdiv_wf
Rules used in proof :
axiomEquality,
because_Cache,
setEquality,
rename,
setElimination,
lambdaEquality,
applyEquality,
hypothesisEquality,
baseClosed,
voidElimination,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
dependent_functionElimination,
hypothesis,
independent_isectElimination,
intEquality,
cumulativity,
instantiate,
lambdaFormation,
addLevel,
natural_numberEquality,
dependent_set_memberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[x:\mBbbR{}]. (sinh(x) \mmember{} \mBbbR{})
Date html generated:
2016_11_08-AM-09_09_26
Last ObjectModification:
2016_10_30-PM-06_41_18
Theory : reals_2
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